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Number Theory

Authors and titles for math.NT in Aug 2021

[ total of 237 entries: 1-237 ]
[ showing 237 entries per page: fewer | more ]
[1]  arXiv:2108.00168 [pdf, ps, other]
Title: Factorization of Hilbert class polynomials over prime fields
Authors: Jianing Li, Songsong Li, Yi Ouyang
Subjects: Number Theory (math.NT)
[2]  arXiv:2108.00287 [pdf, ps, other]
Title: A paucity problem associated with a shifted integer analogue of the divisor function
Authors: Winston Heap, Anurag Sahay, Trevor D. Wooley
Comments: 7 pages
Subjects: Number Theory (math.NT)
[3]  arXiv:2108.00396 [pdf, ps, other]
Title: On the number of zeros of diagonal quartic forms over finite fields
Authors: Junyong Zhao, Yulu Feng, Shaofang Hong, Chaoxi Zhu
Comments: 22 pages
Subjects: Number Theory (math.NT)
[4]  arXiv:2108.00431 [pdf, ps, other]
Title: The distribution of spacings of real-valued lacunary sequences modulo one
Authors: Sneha Chaubey, Nadav Yesha
Comments: 12 pages
Subjects: Number Theory (math.NT)
[5]  arXiv:2108.00545 [pdf, other]
Title: Congruence counting in Schottky and continued fractions semigroups of $\operatorname{SO}(n, 1)$
Authors: Pratyush Sarkar
Comments: 41 pages, 1 figure
Subjects: Number Theory (math.NT); Dynamical Systems (math.DS); Spectral Theory (math.SP)
[6]  arXiv:2108.00549 [pdf, ps, other]
Title: Multidimensional Padé approximation of binomial functions: Equalities
Authors: Michael A. Bennett, Greg Martin, Kevin O'Bryant
Comments: 30 pages, ancillary Mathematica notebook
Journal-ref: Integers 21A (2021), Paper No. A4, 29 pages
Subjects: Number Theory (math.NT); Numerical Analysis (math.NA)
[7]  arXiv:2108.00676 [pdf, ps, other]
Title: Newton polygons for $L$-functions of generalized Kloosterman sums
Authors: Chunlin Wang, Liping Yang
Comments: 19 pages
Subjects: Number Theory (math.NT)
[8]  arXiv:2108.00726 [pdf, ps, other]
Title: Variance estimates in Linnik's problem
Authors: Andrei Shubin
Comments: 48 pages
Subjects: Number Theory (math.NT)
[9]  arXiv:2108.00810 [pdf, ps, other]
Title: Koshliakov zeta functions I: Modular Relations
Authors: Atul Dixit, Rajat Gupta
Comments: 34 pages, submitted for publication; comments are welcome
Subjects: Number Theory (math.NT); Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA)
[10]  arXiv:2108.00811 [pdf, ps, other]
Title: Special values of $L$-functions on regular arithmetic schemes of dimension $1$
Authors: Adrien Morin
Comments: 49 pages
Subjects: Number Theory (math.NT)
[11]  arXiv:2108.00822 [pdf, ps, other]
Title: Extremal product-one free sequences over $C_n \rtimes_s C_2$
Authors: Fabio Enrique Brochero Martínez, Sávio Ribas
Comments: 9 pages. This is a complete answer to the inverse problem proposed in the old versions of the paper "The $\{1,s\}$-weighted Davenport constant in $C_n^k$". In those old versions, partial answers were given using the bounds of the weighted problem. This complete answer does not use any bound obtained there
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[12]  arXiv:2108.00823 [pdf, ps, other]
Title: The main zero-sum constants over $D_{2n} \times C_2$
Authors: Fabio Enrique Brochero Martínez, Abílio Lemos, B. K. Moriya, Sávio Ribas
Comments: 12 pages
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[13]  arXiv:2108.00826 [pdf, ps, other]
Title: Euler sums of generalized alternating hyperharmonic numbers II
Authors: Rusen Li
Comments: 33 pages
Subjects: Number Theory (math.NT)
[14]  arXiv:2108.00840 [pdf, ps, other]
Title: Semi-modular forms from Fibonacci-Eisenstein series
Authors: A. P. Akande, Robert Schneider
Comments: 8 pages, submitted for publication
Subjects: Number Theory (math.NT)
[15]  arXiv:2108.00844 [pdf, ps, other]
Title: Asymptotic expansions for the truncation error in Ramanujan-type series
Authors: Lorenz Milla
Comments: 12 pages, 2 figures (to appear in the Ramanujan Journal); this preprint contains additional 12 pages in the appendix
Journal-ref: Ramanujan Journal (2022), free full-text access via https://rdcu.be/cT2Sz
Subjects: Number Theory (math.NT)
[16]  arXiv:2108.00943 [pdf, other]
Title: Derivatives and Integrals of Polynomials Associated with Integer Partitions
Authors: Madeline Locus Dawsey, Tyler Russell, Dannie Urban
Comments: V1: 17 pages, submitted for publication V2: 18 pages, accepted for publication
Journal-ref: Journal of Integer Sequences, Vol. 25 (2022), Article 22.5.1
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[17]  arXiv:2108.01027 [pdf, ps, other]
Title: Proof of the elliptic expansion Moonshine Conjecture of Căldăraru, He, and Huang
Authors: Letong Hong, Michael H. Mertens, Ken Ono, Shengtong Zhang
Comments: 10 pages. Revised based on the referee's comments. Added reference to work of Shen and Zhou pertaining to Conjecture (1)
Journal-ref: Proc. Am. Math. Soc., 150 (2022), 5047-5056
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Symplectic Geometry (math.SG)
[18]  arXiv:2108.01040 [pdf, ps, other]
Title: Bounds for theta sums in higher rank I
Authors: Jens Marklof, Matthew Welsh
Comments: 27 pages, to be published in Journal d'Analyse Math\'ematique
Subjects: Number Theory (math.NT); Dynamical Systems (math.DS)
[19]  arXiv:2108.01247 [pdf, ps, other]
Title: Integral representations for $ζ(3)$ with the inverse sine function
Authors: Masato Kobayashi
Comments: 9 pages
Subjects: Number Theory (math.NT)
[20]  arXiv:2108.01270 [pdf, other]
Title: Generalized coefficients of the Dirichlet series
Authors: Kirill Kapitonets
Comments: 14 pages, 23 figures
Subjects: Number Theory (math.NT)
[21]  arXiv:2108.01275 [pdf, ps, other]
Title: Spectrum of weighted adjacency operator on a non-uniform arithmetic quotient of $PGL_3$
Authors: Soonki Hong, Sanghoon Kwon
Comments: 21 pages, 3 figures, Any comments welcome! v2: Minor Correction
Journal-ref: Comb. Number Th. 13 (2024) 103-122
Subjects: Number Theory (math.NT); Combinatorics (math.CO); Group Theory (math.GR)
[22]  arXiv:2108.01302 [pdf, ps, other]
Title: Bohr neighborhoods in generalized difference sets
Authors: John T. Griesmer
Comments: 17 pages
Subjects: Number Theory (math.NT); Combinatorics (math.CO); Dynamical Systems (math.DS)
[23]  arXiv:2108.01355 [pdf, ps, other]
Title: Exceptional characters and prime numbers in sparse sets
Authors: Jori Merikoski
Subjects: Number Theory (math.NT)
[24]  arXiv:2108.01484 [pdf, ps, other]
Title: On Wirsing's problem in small exact degree
Authors: Johannes Schleischitz
Comments: 29 pages ; In particular closes a gap in erroneous proof of Theorem 3.2 in arXiv:1701.01129
Subjects: Number Theory (math.NT)
[25]  arXiv:2108.01540 [pdf, ps, other]
Title: On the new identities of Dirichlet $L$-functions
Authors: Rong Ma, Jinglei Zhang, Yulong Zhang
Comments: 10 pages
Subjects: Number Theory (math.NT)
[26]  arXiv:2108.01822 [pdf, ps, other]
Title: Möbius functions of higher rank and Dirichlet series
Authors: Masato Kobayashi
Comments: 17 pages
Subjects: Number Theory (math.NT)
[27]  arXiv:2108.01827 [pdf, ps, other]
Title: On a new class of Laguerre-Pólya type functions with applications in number theory
Authors: Ian Wagner
Journal-ref: Pacific J. Math. 320 (2022) 177-192
Subjects: Number Theory (math.NT)
[28]  arXiv:2108.01904 [src]
Title: Pólya-Ostrowski Group and Unit Index in Real Biquadratic Fields
Authors: Abbas Maarefparvar
Comments: I recently have found that some results in this draft has been already obtained by my colleagues. Their paper is now submitted and I hope to be published early
Subjects: Number Theory (math.NT)
[29]  arXiv:2108.02024 [pdf, ps, other]
Title: Well-defined Erdös-Straus equations and L.C.M
Authors: Mohammad Arab
Comments: 71pages
Subjects: Number Theory (math.NT)
[30]  arXiv:2108.02086 [pdf, ps, other]
Title: More Arithmetic Fundamental Lemma conjectures: the case of Bessel subgroups
Authors: Wei Zhang
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Representation Theory (math.RT)
[31]  arXiv:2108.02111 [pdf, ps, other]
Title: Algebraicity of critical values of triple product $L$-functions in the balanced case
Authors: Shih-Yu Chen
Subjects: Number Theory (math.NT)
[32]  arXiv:2108.02227 [pdf, ps, other]
Title: Difference sets and the metric theory of small gaps
Authors: Christoph Aistleitner, Daniel El-Baz, Marc Munsch
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[33]  arXiv:2108.02301 [pdf, ps, other]
Title: Extreme values of derivatives of the Riemann zeta function
Authors: Daodao Yang
Comments: 27 pages
Subjects: Number Theory (math.NT)
[34]  arXiv:2108.02342 [pdf, ps, other]
Title: New relations on zeta and $L$ functions
Authors: Masato Kobayashi
Comments: 14 pages
Subjects: Number Theory (math.NT)
[35]  arXiv:2108.02435 [pdf, ps, other]
Title: Ome new theorems on generating functions and their applications on odd and even certain numbers attached to p and q parameters
Authors: N.Saba, a. Boussayoud
Subjects: Number Theory (math.NT)
[36]  arXiv:2108.02441 [pdf, ps, other]
Title: Equations of the Cayley Surface
Authors: Matty van Son
Subjects: Number Theory (math.NT)
[37]  arXiv:2108.02640 [pdf, ps, other]
Title: Fruit Diophantine Equation
Authors: Dipramit Majumdar, B. Sury
Comments: 3 pages, couple of typos fixed
Subjects: History and Overview (math.HO); Number Theory (math.NT)
[38]  arXiv:2108.02823 [pdf, ps, other]
Title: Modularity of trianguline Galois representations
Authors: Rebecca Bellovin
Comments: Final version. To appear in Forum Math., Sigma
Subjects: Number Theory (math.NT)
[39]  arXiv:2108.02919 [pdf, other]
Title: Eisenstein series on arithmetic quotients of rank 2 Kac--Moody groups over finite fields, with an appendix by Paul Garrett
Authors: Abid Ali, Lisa Carbone
Subjects: Number Theory (math.NT); Group Theory (math.GR)
[40]  arXiv:2108.03123 [pdf, ps, other]
Title: Integral points in orbits in characteristic $p$
Authors: Alexander Carney, Wade Hindes, Thomas J. Tucker
Comments: 19 pages
Journal-ref: Alg. Number Th. 17 (2023) 1573-1594
Subjects: Number Theory (math.NT); Dynamical Systems (math.DS)
[41]  arXiv:2108.03198 [pdf, ps, other]
Title: Integer circulant determinants of order 15
Authors: Bishnu Paudel, Chris Pinner
Subjects: Number Theory (math.NT)
[42]  arXiv:2108.03261 [pdf, ps, other]
Title: Quasi-inner automorphisms of Drinfeld modular groups
Authors: A. W. Mason, Andreas Schweizer
Comments: 32 pages
Journal-ref: Groups, Geometry, and Dynamics, vol 18, no. 2 (2024), 571-602
Subjects: Number Theory (math.NT); Group Theory (math.GR)
[43]  arXiv:2108.03268 [pdf, ps, other]
Title: Series and Product Relations Made from Primes
Authors: Ken Hicks, Kevin Ward
Comments: 9 pages, no figures
Journal-ref: Pi Mu Epsilon, Volume 15, No. 3, Fall 2020, pp. 161-169
Subjects: Number Theory (math.NT)
[44]  arXiv:2108.03286 [pdf, other]
Title: Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of $\mathbb{F_p}$
Authors: Ali Alsetri, Xuancheng Shao
Subjects: Number Theory (math.NT)
[45]  arXiv:2108.03367 [pdf, ps, other]
Title: Normal integral bases and Gaussian periods in the simplest cubic fields
Authors: Yu Hashimoto, Miho Aoki
Subjects: Number Theory (math.NT)
[46]  arXiv:2108.03393 [pdf, ps, other]
Title: Properties of Trinomials of Height at least 2
Authors: V. Flammang, P. Voutier
Comments: submitted version, comments very welcome!
Subjects: Number Theory (math.NT)
[47]  arXiv:2108.03395 [pdf, other]
Title: Diagonal cubic forms and the large sieve
Authors: Victor Y. Wang
Comments: 23 pages; added references; improved exposition; moved some material elsewhere
Subjects: Number Theory (math.NT)
[48]  arXiv:2108.03396 [pdf, other]
Title: Special cubic zeros and the dual variety
Authors: Victor Y. Wang
Comments: 30 pages; added references; changed title; conceptual improvements
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[49]  arXiv:2108.03398 [pdf, other]
Title: Sums of cubes and the Ratios Conjectures
Authors: Victor Y. Wang
Comments: 61 pages; updated references; changed title; conceptual improvements; moved some material elsewhere
Subjects: Number Theory (math.NT); Mathematical Physics (math-ph); Algebraic Geometry (math.AG)
[50]  arXiv:2108.03520 [pdf, ps, other]
Title: An unconditional explicit bound on the error term in the Sato-Tate conjecture
Authors: Alexandra Hoey, Jonas Iskander, Steven Jin, Fernando Trejos Suárez
Comments: 31 pages; minor improvements in exposition; minor typos fixed
Subjects: Number Theory (math.NT)
[51]  arXiv:2108.03525 [pdf, ps, other]
Title: On an equation by primes with one Linnik prime
Authors: S. I. Dimitrov
Comments: arXiv admin note: substantial text overlap with arXiv:2107.04028, arXiv:2012.06476, arXiv:2011.03967
Subjects: Number Theory (math.NT)
[52]  arXiv:2108.03584 [pdf, ps, other]
Title: The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$
Authors: Maria Fox, Naoki Imai
Comments: 28 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[53]  arXiv:2108.03628 [pdf, ps, other]
Title: On the l.c.m. of shifted Lucas numbers
Authors: Carlo Sanna
Subjects: Number Theory (math.NT); Probability (math.PR)
[54]  arXiv:2108.03651 [pdf, ps, other]
Title: Daehee, hyperharmonic, and power sums polynomials
Authors: José L. Cereceda
Comments: 22 pages
Subjects: Number Theory (math.NT)
[55]  arXiv:2108.03664 [pdf, ps, other]
Title: On the existence of numbers with matching continued fraction and decimal expansions
Authors: Pieter Allaart, Stephen Jackson, Taylor Jones, David Lambert
Comments: 30 pages, new title and a somewhat expanded introduction
Subjects: Number Theory (math.NT)
[56]  arXiv:2108.03716 [pdf, other]
Title: A dynamic approach for the zeros of the Riemann zeta function - collision and repulsion
Authors: Yochay Jerby
Comments: 24 pages, 11 figures
Subjects: Number Theory (math.NT)
[57]  arXiv:2108.03750 [pdf, ps, other]
Title: The $p$-adic Kakeya conjecture
Authors: Bodan Arsovski
Comments: Style
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG)
[58]  arXiv:2108.03753 [pdf, ps, other]
Title: Sums of powers and special polynomials
Authors: Khristo N. Boyadzhiev
Comments: 10 pages
Journal-ref: Discussiones Mathematicae, General Algebra ans Applications, 20 (2020), 275-283;
Subjects: Number Theory (math.NT)
[59]  arXiv:2108.03833 [pdf, ps, other]
Title: Crystalline condition for $A_{\mathrm{inf}}$-cohomology and ramification bounds
Authors: Pavel Čoupek
Comments: 37 pages. Revised version. Added a discussion of finiteness conditions in the construction of \v{C}ech-Alexander complexes (Remarks 2.13, 2.17, Lemma 2.18) and appropriate adjustment of related constructions in \S 4.1. Other minor modifications and updates
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[60]  arXiv:2108.03932 [pdf, ps, other]
Title: Sign Changes of Coefficients of Powers of the Infinite Borwein Product
Authors: Liuquan Wang
Comments: 28 pages (including an Appendix with 5 pages). This paper has been rewritten after its first version (v1) with a different title. We found that the results in v1 can be generalized and thus rewrote it in v2. Minor changes will be made after v2. Please do not cite v1
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[61]  arXiv:2108.03985 [pdf, ps, other]
Title: Simultaneous non-vanishing of central values of $GL(2) \times GL(3) $ and $GL(3)$ $L$-functions
Authors: Gopal Maiti, Kummari Mallesham
Comments: Comments are welcome!
Subjects: Number Theory (math.NT)
[62]  arXiv:2108.04094 [pdf, ps, other]
Title: Degenerating products of flag varieties and applications to the Breuil--Mezard conjecture
Authors: Robin Bartlett
Comments: Fixed some small mistakes
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Representation Theory (math.RT)
[63]  arXiv:2108.04120 [pdf, other]
Title: Eisenstein Metrics
Authors: Cameron Franc
Comments: 24 pages, 1 figure, 1 table
Subjects: Number Theory (math.NT); Differential Geometry (math.DG)
[64]  arXiv:2108.04155 [pdf, ps, other]
Title: The structure of weight and function classes with coprime bases
Authors: Theresa C. Anderson, Chiara Travesset, Joey Veltri
Journal-ref: The Quarterly Journal of Mathematics (2022)
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
[65]  arXiv:2108.04171 [pdf, ps, other]
Title: Arithmetic of some real triquadratic fields; Units and 2-class groups
Authors: Mohamed Mahmoud Chems-Eddin
Comments: This is a new revised version, 33 pages
Subjects: Number Theory (math.NT)
[66]  arXiv:2108.04270 [pdf, ps, other]
Title: Non-isogenous abelian varieties sharing the same division fields
Authors: Davide Lombardo
Comments: 22 pages, includes some unpublished parts of arXiv:1402.1478. Comments are very welcome!
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[67]  arXiv:2108.04411 [pdf, ps, other]
Title: Heights and quantitative arithmetic on stacky curves
Authors: Brett Nasserden, Stanley Yao Xiao
Comments: This subsumes our earlier paper arXiv:2011.06586
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[68]  arXiv:2108.04502 [pdf, ps, other]
Title: Invariant generalized ideal classes -- structure theorems for p-class groups in p-extensions
Authors: Georges Gras (LMB)
Journal-ref: Proceedings Mathematical Sciences, Indian Academy of Sciences, 2017, Proceedings - Mathematical Sciences, 127 (1), pp.1-34
Subjects: Number Theory (math.NT)
[69]  arXiv:2108.04535 [pdf, ps, other]
Title: On the Decomposition of Hecke Polynomials over Parabolic Hecke Algebras
Authors: Claudius Heyer
Comments: 41 pages, 4 figures. Comments welcome! v2: small changes according to suggestions of the referee
Journal-ref: Journal de th\'eorie des nombres de Bordeaux, Volume 34 (2022) no. 3, pp. 941-997
Subjects: Number Theory (math.NT)
[70]  arXiv:2108.04638 [pdf, ps, other]
Title: A measure estimate in geometry of numbers and improvements to Dirichlet's theorem
Authors: Dmitry Kleinbock, Andreas Strömbergsson, Shucheng Yu
Comments: 39 pages; minor revisions
Subjects: Number Theory (math.NT); Dynamical Systems (math.DS)
[71]  arXiv:2108.04662 [pdf, ps, other]
Title: Properties of Higher-Order Prime Number Sequences
Authors: Michael P. May
Comments: 13 pages, 1 figure
Journal-ref: MISSOURI J. OF MATH. SCI., FALL 2020, VOL. 32, NO. 2
Subjects: Number Theory (math.NT)
[72]  arXiv:2108.04756 [pdf, ps, other]
Title: On the number of integer non-negative solutions of a linear Diophantine equation
Authors: Eteri Samsonadze
Comments: 20 pages
Subjects: Number Theory (math.NT)
[73]  arXiv:2108.04870 [pdf, ps, other]
Title: The Integer group determinants for the Heisenberg group of order $p^3$
Authors: Michael J. Mossinghoff, Christopher Pinner
Subjects: Number Theory (math.NT)
[74]  arXiv:2108.04968 [pdf, ps, other]
Title: On sum of Hecke eigenvalue squares over primes in very short intervals
Authors: Jiseong Kim
Comments: Minor corrections. to appear in Acta Arithmetica
Subjects: Number Theory (math.NT)
[75]  arXiv:2108.05007 [pdf, other]
Title: Ghost distributions of regular sequences are affine transformations of self-affine sets
Authors: Michael Coons, James Evans, Zachary Groth, Neil Mañibo
Comments: 15 pages
Subjects: Number Theory (math.NT); Dynamical Systems (math.DS)
[76]  arXiv:2108.05049 [pdf, ps, other]
Title: Representing polynomials by degenerate Bernoulli polynomials
Authors: Dae san Kim, Taekyun Kim
Comments: 19 pages
Subjects: Number Theory (math.NT)
[77]  arXiv:2108.05235 [pdf, ps, other]
Title: Geometric quadratic Chabauty over number fields
Authors: Pavel Čoupek, David T.-B. G. Lilienfeldt, Zijian Yao, Luciena Xiao Xiao
Comments: Accepted Manuscript, to appear in Transactions of the American Mathematical Society. Minor changes in Section 7
Journal-ref: Trans. Amer. Math. Soc. 376 (2023), no. 4, 2573-2613
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[78]  arXiv:2108.05262 [pdf, ps, other]
Title: On the Smooth Part Functor
Authors: Claudius Heyer
Comments: 4 pages. Comments welcome!
Subjects: Number Theory (math.NT); Representation Theory (math.RT)
[79]  arXiv:2108.05496 [pdf, ps, other]
Title: Distribution of residues of an algebraic number modulo ideals of degree one
Authors: Chunlin Wang
Subjects: Number Theory (math.NT)
[80]  arXiv:2108.05591 [pdf, ps, other]
Title: Higher Ext-groups and Relatively Supercuspidal Spectra
Authors: Li Cai, Yangyu Fan
Subjects: Number Theory (math.NT); Representation Theory (math.RT)
[81]  arXiv:2108.05592 [pdf, ps, other]
Title: Bianchi modular symbols and $p$-adic $L$-functions
Authors: Jaesung Kwon
Comments: to be updated
Subjects: Number Theory (math.NT)
[82]  arXiv:2108.05625 [pdf, ps, other]
Title: Arithmetic bigness and a uniform Bogomolov-type result
Authors: Xinyi Yuan
Comments: 125 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[83]  arXiv:2108.05688 [pdf, ps, other]
Title: Totally real bi-quadratic fields with large Pólya groups
Authors: Jaitra Chattopadhyay, Anupam Saikia
Comments: 7 pages
Subjects: Number Theory (math.NT)
[84]  arXiv:2108.05777 [pdf, ps, other]
Title: Divergent Integrals of Certain Analytical Functions In the Sense of Zeta Regularization
Authors: Farhad Aghili
Comments: 6 pages
Subjects: Number Theory (math.NT)
[85]  arXiv:2108.05794 [pdf, ps, other]
Title: On the number of zeros to the equation $f(x_1)+...+f(x_n)=a$ over finite fields
Authors: Chaoxi Zhu, Yulu Feng, Shaofang Hong, Junyong Zhao
Comments: 13 pages
Subjects: Number Theory (math.NT)
[86]  arXiv:2108.05958 [pdf, ps, other]
Title: The vanishing of anticyclotomic $μ$-invariants for non-ordinary modular forms
Authors: Jeffrey Hatley, Antonio Lei
Comments: To appear in Comptes Rendus Mathematique
Subjects: Number Theory (math.NT)
[87]  arXiv:2108.06034 [pdf, ps, other]
Title: Factorization of measures and applications to the weak Goldfeld conjecture
Authors: Merrick Cai
Comments: 24 pages
Subjects: Number Theory (math.NT)
[88]  arXiv:2108.06260 [pdf, ps, other]
Title: Some new properties on degenerate Bell polynomials
Authors: Taekyun Kim, Dae San Kim, Hyunseok Lee, Seongho Park
Comments: 13 pages
Subjects: Number Theory (math.NT)
[89]  arXiv:2108.06292 [pdf, ps, other]
Title: The Lang-Trotter Conjecture for the elliptic curve $y^2=x^3+Dx$
Authors: Hourong Qin
Subjects: Number Theory (math.NT)
[90]  arXiv:2108.06319 [pdf, ps, other]
Title: Modular Proofs of Gosper's Identities
Authors: Liuquan Wang
Comments: 22 pages. Minor changes may be made after v2
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA); Combinatorics (math.CO)
[91]  arXiv:2108.06358 [pdf, other]
Title: Asymptotic Density of Apollonian-Type Packings
Authors: Matthew Litman, Arseniy Sheydvasser
Subjects: Number Theory (math.NT)
[92]  arXiv:2108.06369 [pdf, ps, other]
Title: On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations
Authors: Harald Grobner, Sonja Žunar
Subjects: Number Theory (math.NT)
[93]  arXiv:2108.06402 [pdf, other]
Title: Comparing Two Formulas for the Gross-Stark Units
Authors: Matthew H. Honnor
Comments: 40 pages, 4 figures
Subjects: Number Theory (math.NT)
[94]  arXiv:2108.06433 [pdf, other]
Title: Modular forms, projective structures, and the four squares theorem
Authors: Michael Eastwood, Ben Moore
Comments: 24 pages
Subjects: Number Theory (math.NT); Differential Geometry (math.DG)
[95]  arXiv:2108.06540 [pdf, ps, other]
Title: On analytic properties of the standard zeta function attached to a vector valued modular form
Authors: Oliver Stein
Comments: 28 pages, submitted for publication
Subjects: Number Theory (math.NT)
[96]  arXiv:2108.06544 [pdf, ps, other]
Title: On vector valued automorphic forms and the standard $L$-function attached to them
Authors: Oliver Stein
Comments: 44 pages, submitted for publication
Subjects: Number Theory (math.NT)
[97]  arXiv:2108.06549 [pdf, ps, other]
Title: Correction and addendum to: The Fourier expansion of Hecke operators for vector-valued modular forms
Authors: Oliver Stein
Comments: 9 pages, submitted for publication
Subjects: Number Theory (math.NT)
[98]  arXiv:2108.06560 [pdf, ps, other]
Title: Hyperelliptic continued fractions in the singular case of genus zero
Authors: Francesco Ballini, Francesco Veneziano
Subjects: Number Theory (math.NT)
[99]  arXiv:2108.06586 [pdf, ps, other]
Title: The birthday boy problem
Authors: Wadim Zudilin
Comments: 4 pages; typos corrected in version 2
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA); Combinatorics (math.CO)
[100]  arXiv:2108.06656 [pdf, ps, other]
Title: On fine Selmer groups and signed Selmer groups of elliptic modular forms
Authors: Antonio Lei, Meng Fai Lim
Comments: Some minor corrections and updates on references
Journal-ref: Bulletin of the Australian Mathematical Society 105 (2022), no. 3, 419-430
Subjects: Number Theory (math.NT)
[101]  arXiv:2108.06732 [pdf, ps, other]
Title: Zariski dense orbits for regular self-maps of split semiabelian varieties in positive characteristic
Authors: Dragos Ghioca, Sina Saleh
Subjects: Number Theory (math.NT)
[102]  arXiv:2108.06754 [pdf, ps, other]
Title: Hypergeometric functions over finite fields
Authors: Noriyuki Otsubo
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
[103]  arXiv:2108.06799 [pdf, ps, other]
Title: Constructive representation of primitive Pythagorean triples
Authors: Natalia Aleshkevich
Comments: 13 pages, 6 figures
Subjects: Number Theory (math.NT)
[104]  arXiv:2108.06804 [pdf, ps, other]
Title: On a question of Mendès France on normal numbers
Authors: Verónica Becher, Manfred G. Madritsch
Comments: 15 pages. arXiv admin note: text overlap with arXiv:1704.03622
Subjects: Number Theory (math.NT)
[105]  arXiv:2108.06998 [pdf, other]
Title: Deformation of rigid conjugate self-dual Galois representations
Authors: Yifeng Liu, Yichao Tian, Liang Xiao, Wei Zhang, Xinwen Zhu
Comments: 42 pages. This article is essentially the original Appendix E of the article arXiv:1912.11942; we now decide to make that appendix an independent article
Subjects: Number Theory (math.NT)
[106]  arXiv:2108.07029 [pdf, ps, other]
Title: On $p$-adic Simpson and Riemann-Hilbert correspondences in the imperfect residue field case
Authors: Hui Gao
Comments: v2: minor revision
Subjects: Number Theory (math.NT)
[107]  arXiv:2108.07042 [pdf, ps, other]
Title: On the minimum size of subset and subsequence sums in integers
Authors: Jagannath Bhanja, Ram Krishna Pandey
Comments: Corrected version
Journal-ref: Comptes Rendus Mathematique, Volume 360 (2022), pp. 1099-1111
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[108]  arXiv:2108.07264 [pdf, ps, other]
Title: A model problem for multiplicative chaos in number theory
Authors: Kannan Soundararajan, Asif Zaman
Comments: 25 pages
Journal-ref: Enseign. Math. 68 (2022), no. 3, 307-340
Subjects: Number Theory (math.NT); Probability (math.PR)
[109]  arXiv:2108.07373 [pdf, ps, other]
Title: The existence of $\mathbb{F}_q$-primitive points on curves using freeness
Authors: Stephen D. Cohen, Giorgos Kapetanakis, Lucas Reis
Subjects: Number Theory (math.NT)
[110]  arXiv:2108.07557 [pdf, ps, other]
Title: Moments of Traces of Frobenius of Higher Order Dirichlet $L$-functions over $\mathbb{F}_q[T]$
Authors: Patrick Meisner
Subjects: Number Theory (math.NT)
[111]  arXiv:2108.07577 [pdf, ps, other]
Title: A simplified proof of Serre's Conjectures
Authors: Luis Victor Dieulefait, Ariel Martín Pacetti
Comments: 11 pages
Subjects: Number Theory (math.NT)
[112]  arXiv:2108.07608 [pdf, ps, other]
Title: Integral $p$-adic cohomology theories
Authors: Tomoyuki Abe, Richard Crew
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[113]  arXiv:2108.07617 [pdf, ps, other]
Title: Representations of almost regular m-gonal forms II
Authors: Dayoon Park
Subjects: Number Theory (math.NT)
[114]  arXiv:2108.07677 [pdf, ps, other]
Title: Generalizations of Lerch's formula by Barnes' multiple zeta functions
Authors: Su Hu, Min-Soo Kim
Comments: 10 pages
Subjects: Number Theory (math.NT); Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA)
[115]  arXiv:2108.08049 [pdf, ps, other]
Title: Euclidean algorithm in Galois Quartic Fields
Authors: K Srinivas, M Subramani, Usha K Sangale
Comments: 7 pages
Subjects: Number Theory (math.NT)
[116]  arXiv:2108.08066 [pdf, ps, other]
Title: The trace of primitive and $2$-primitive elements in finite fields, revisited
Authors: Stephen D. Cohen, Giorgos Kapetanakis
Comments: arXiv admin note: substantial text overlap with arXiv:1903.03160
Subjects: Number Theory (math.NT)
[117]  arXiv:2108.08107 [pdf, ps, other]
Title: Invariants for the Weil representation and Modular Units for Orthogonal Groups of Signature (2,2)
Authors: Patrick Bieker
Comments: 24 pages, final version, to appear in Journal of Number Theory
Journal-ref: Journal of Number Theory, Volume 250, 2023, pp. 155-182
Subjects: Number Theory (math.NT)
[118]  arXiv:2108.08171 [pdf, other]
Title: Further insights into the mysteries of the values of zeta functions at integers
Authors: Ján Mináč, Nguyen Duy Tân, Nguyen Tho Tung
Comments: To appear in Mathematica Slovaca
Subjects: Number Theory (math.NT)
[119]  arXiv:2108.08232 [pdf, ps, other]
Title: Sums of random multiplicative functions over function fields with few irreducible factors
Authors: Daksh Aggarwal, Unique Subedi, William Verreault, Asif Zaman, Chenghui Zheng
Comments: 10 pages. Simplification of the proof of Lemma 5 and typos corrected, one reference added
Journal-ref: Math. Proc. Camb. Phil. Soc. (2022), 1-12
Subjects: Number Theory (math.NT)
[120]  arXiv:2108.08337 [pdf, ps, other]
Title: Class fields, Dirichlet characters and extended genus fields of global function fields
Authors: Martha Rzedowski-Calderón, Gabriel Villa-Salvador
Comments: 16 pages. arXiv admin note: text overlap with arXiv:1901.07156
Subjects: Number Theory (math.NT)
[121]  arXiv:2108.08534 [pdf, ps, other]
Title: Multiple $T$-values with one parameter
Authors: Frédéric Chapoton (IRMA)
Comments: 8 pages, pas de figure
Subjects: Number Theory (math.NT)
[122]  arXiv:2108.08572 [pdf, ps, other]
Title: Semilocal approximation for the Fermat-Catalan and further popular Diophantine norm equations
Authors: Boris Bartolomé, Preda Mihailescu
Comments: Submitted, under review
Subjects: Number Theory (math.NT)
[123]  arXiv:2108.08580 [pdf, ps, other]
Title: Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem
Authors: Preda Mihăilescu, Michael T. Rassias
Comments: Submitted, under review
Subjects: Number Theory (math.NT)
[124]  arXiv:2108.08634 [pdf, ps, other]
Title: q-analogues of multiple zeta values and the formal double Eisenstein space
Authors: Henrik Bachmann
Comments: 13 pages, Survey article for the 2021 Waseda number theory Conference Proceedings
Subjects: Number Theory (math.NT)
[125]  arXiv:2108.08727 [pdf, ps, other]
Title: Elliptic curves with missing Frobenius traces
Authors: Nathan Jones, Kevin Vissuet
Subjects: Number Theory (math.NT)
[126]  arXiv:2108.08778 [pdf, ps, other]
Title: Über Approximationen $n$ reeller Zahlen
Authors: Vassily Manturov, Nikolay Moshchevitin
Comments: in German, this version contains minor corrections
Subjects: Number Theory (math.NT)
[127]  arXiv:2108.09001 [pdf, ps, other]
Title: Counting $3$-dimensional algebraic tori over $\mathbb{Q}$
Authors: Jungin Lee
Comments: 33 pages, to appear in J. Number Theory
Journal-ref: Journal of Number Theory 249 (2023), 49-92
Subjects: Number Theory (math.NT)
[128]  arXiv:2108.09006 [pdf, ps, other]
Title: Centrality of the congruence subgroup kernel of higher rank non-uniform arithmetic groups
Authors: Tyakal N.Venkataramana
Comments: 28 pages
Subjects: Number Theory (math.NT); Group Theory (math.GR)
[129]  arXiv:2108.09013 [pdf, ps, other]
Title: Arithmetic over the Gaussian Number Field on a Certain Family of Elliptic Curves with Complex Multiplication
Authors: Yoshihiro Ônishi, Fumio Sairaiji
Comments: 22 pages. submitted to RIMS K\^oky\^uroku Bessatsu
Subjects: Number Theory (math.NT)
[130]  arXiv:2108.09191 [pdf, ps, other]
Title: Overconvergent cohomology, $p$-adic $L$-functions and families for $\mathrm{GL}(2)$ over CM fields
Authors: Daniel Barrera Salazar, Chris Williams
Comments: 31 pages, final version. To appear in Journal de Theorie des Nombres de Bordeaux (Iwasawa 2019 special issue)
Journal-ref: J. Th\'eor. Nomb. Bordeaux, 33 (2021), no.3, pp.659-701
Subjects: Number Theory (math.NT)
[131]  arXiv:2108.09212 [pdf, ps, other]
Title: Primes with a missing digit: distribution in arithmetic progressions and an application in sieve theory
Authors: Kunjakanan Nath
Comments: Accepted version, fixed a few typos, rewrote parts III and IV, a small necessary fix in the proof of Lemma 6.2 was applied
Subjects: Number Theory (math.NT)
[132]  arXiv:2108.09258 [pdf, other]
Title: On Montgomery's pair correlation conjecture: a tale of three integrals
Authors: Emanuel Carneiro, Vorrapan Chandee, Andrés Chirre, Micah B. Milinovich
Comments: 38 pages, 5 figures; v2 typos corrected. To appear in Journal f\"{u}r die reine und angewandte Mathematik
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
[133]  arXiv:2108.09333 [pdf, other]
Title: Dynatomic polynomials, necklace operators, and universal relations for dynamical units
Authors: John R. Doyle, Paul Fili, Trevor Hyde
Comments: 19 pages, comments welcome!
Journal-ref: New York J. Math. 28 (2022) 534-556
Subjects: Number Theory (math.NT); Dynamical Systems (math.DS)
[134]  arXiv:2108.09410 [pdf, ps, other]
Title: Analytic twists of $\rm GL_2\times\rm GL_2$ automorphic forms
Authors: Bingrong Huang, Qingfeng Sun, Huimin Zhang
Comments: 30 pages. Comments welcome! arXiv admin note: text overlap with arXiv:1912.09772
Subjects: Number Theory (math.NT)
[135]  arXiv:2108.09492 [pdf, ps, other]
Title: Local Solubility of Hyperelliptic Curves
Authors: Omri Faraggi
Subjects: Number Theory (math.NT)
[136]  arXiv:2108.09560 [pdf, other]
Title: Distribution of values of Gaussian hypergeometric functions
Authors: Ken Ono, Hasan Saad, Neelam Saikia
Comments: Corrects minor typographical errors. This paper will appear in Don Zagier's 70th Birthday special issue of Pure and Applied Mathematics Quarterly
Subjects: Number Theory (math.NT)
[137]  arXiv:2108.09564 [pdf, ps, other]
Title: $2^\infty$-Selmer Rank Parities via the Prym Construction
Authors: Jordan Docking
Comments: 11 pages
Subjects: Number Theory (math.NT)
[138]  arXiv:2108.09570 [pdf, ps, other]
Title: Towards an Elementary Formulation of the Riemann Hypothesis in Terms of Permutation Groups
Authors: Jacob Tsimerman, Will Cavendish
Comments: 8 pages, comments welcome!
Subjects: Number Theory (math.NT)
[139]  arXiv:2108.09577 [pdf, ps, other]
Title: A Lehmer-type height lower bound for abelian surfaces over function fields
Authors: Nicole R. Looper, Joseph H. Silverman
Comments: 48 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Dynamical Systems (math.DS)
[140]  arXiv:2108.09729 [pdf, ps, other]
Title: Wiles defect of Hecke algebras via local-global arguments
Authors: Gebhard Boeckle, Chandrashekhar B. Khare, Jeffrey Manning
Comments: with an appendix by Najmuddin Fakhruddin and Chandrashekhar Khare
Subjects: Number Theory (math.NT)
[141]  arXiv:2108.09857 [pdf, ps, other]
Title: Uniform explicit Stewart's theorem on prime factors of linear recurrences
Authors: Yuri Bilu, Haojie Hong, Sanoli Gun
Subjects: Number Theory (math.NT)
[142]  arXiv:2108.10142 [pdf, ps, other]
Title: On the sum of digits of $1/M$ in $\mathbb{F}_q[x]$
Authors: Zeev Rudnick
Subjects: Number Theory (math.NT)
[143]  arXiv:2108.10238 [pdf, ps, other]
Title: On the $q$-analogue of the pair correlation conjecture via Fourier optimization
Authors: Emily Quesada-Herrera
Comments: 17 pages, 3 figures. Minor edits. To appear in Math. Comp
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
[144]  arXiv:2108.10247 [pdf, ps, other]
Title: Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function
Authors: D. Essouabri, C. Salinas Zavala, L. Tóth
Comments: 36 pages, to appear in Journal of Number Theory
Subjects: Number Theory (math.NT)
[145]  arXiv:2108.10401 [pdf, ps, other]
Title: Quadratic forms in 8 prime variables
Authors: Ben Green
Comments: 55 pages
Subjects: Number Theory (math.NT); Representation Theory (math.RT)
[146]  arXiv:2108.10439 [pdf, ps, other]
Title: Large Weyl sums and Hausdorff dimension
Authors: Roger C. Baker, Changhao Chen, Igor E. Shparlinski
Comments: 51 pages, 0 figures
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
[147]  arXiv:2108.10553 [pdf, ps, other]
Title: Some implications of the Gessel identity
Authors: Claire Levaillant
Comments: 36 pages, 40 references
Subjects: Number Theory (math.NT)
[148]  arXiv:2108.10624 [pdf, ps, other]
Title: A conjecture of Zhi-Wei Sun on determinants over finite fields
Authors: Hai-Liang Wu, Yue-Feng She, He-Xia Ni
Subjects: Number Theory (math.NT)
[149]  arXiv:2108.10754 [pdf, ps, other]
Title: Bicyclic commutator quotients with one non-elementary component
Authors: Daniel C. Mayer
Comments: 22 pages, 7 tables, 7 figures
Subjects: Number Theory (math.NT); Group Theory (math.GR)
[150]  arXiv:2108.10756 [pdf, ps, other]
Title: Derivation of Computational Formulas for certain class of finite sums: Approach to Generating functions arising from $p$-adic integrals and special functions
Authors: Yilmaz Simsek
Comments: 33
Journal-ref: Mathematical Methods in the Applied Sciences 2022. 45 pp. 9520..9544
Subjects: Number Theory (math.NT)
[151]  arXiv:2108.10845 [pdf, ps, other]
Title: Non-almost regular quaternary $m$-gonal forms
Authors: Dayoon Park
Subjects: Number Theory (math.NT)
[152]  arXiv:2108.10863 [pdf, ps, other]
Title: A note on rational numbers and certain operators
Authors: Symon Serbenyuk
Comments: 7 pages
Subjects: Number Theory (math.NT)
[153]  arXiv:2108.10878 [pdf, ps, other]
Title: Refinements to the prime number theorem for arithmetic progressions
Authors: Jesse Thorner, Asif Zaman
Comments: 11 pages. Theorems 1.1 and 2.1 improved
Journal-ref: Math. Z. 306 (2024), no. 3, Paper No. 54
Subjects: Number Theory (math.NT)
[154]  arXiv:2108.10953 [pdf, ps, other]
Title: Heights of Rational Points on Mordell Curves
Authors: Alan Zhao
Comments: 14 pages
Subjects: Number Theory (math.NT)
[155]  arXiv:2108.11016 [pdf, ps, other]
Title: On the Number of 2-Hooks and 3-Hooks of Integer Partitions
Authors: Eleanor Mcspirit, Kristen Scheckelhoff
Comments: 7 pages
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[156]  arXiv:2108.11090 [pdf, ps, other]
Title: Some identities of fully degenerate Dowling and fully degenerate Bell polynomials arising from lambda-umbral calculus
Authors: Yuankui Ma, Taekyun Kim, Hyunseok Lee, Dae San Kim
Comments: 14 pages
Subjects: Number Theory (math.NT)
[157]  arXiv:2108.11162 [pdf, ps, other]
Title: Small gaps in the spectrum of tori: asymptotic formulae
Authors: Valentin Blomer, Maksym Radziwiłł
Comments: 24 pages
Subjects: Number Theory (math.NT); Mathematical Physics (math-ph); Spectral Theory (math.SP)
[158]  arXiv:2108.11233 [pdf, ps, other]
Title: Galois groups and prime divisors in random quadratic sequences
Authors: John R. Doyle, Vivian Olsiewski Healey, Wade Hindes, Rafe Jones
Comments: 22 pages
Subjects: Number Theory (math.NT); Dynamical Systems (math.DS)
[159]  arXiv:2108.11367 [pdf, other]
Title: A conjectural asymptotic formula for multiplicative chaos in number theory
Authors: Daksh Aggarwal, Unique Subedi, William Verreault, Asif Zaman, Chenghui Zheng
Comments: 18 pages
Journal-ref: Res. Number Theory 8, 35 (2022)
Subjects: Number Theory (math.NT); Probability (math.PR)
[160]  arXiv:2108.11382 [pdf, other]
Title: Fractions, Functions and Folding. A Novel Link between Continued Fractions, Mahler Functions and Paper Folding
Authors: Joris Nieuwveld
Comments: 57 pages, 7 figures. Master's Thesis
Subjects: Number Theory (math.NT); Combinatorics (math.CO); Complex Variables (math.CV)
[161]  arXiv:2108.11401 [pdf, ps, other]
Title: Divisor-bounded multiplicative functions in short intervals
Authors: Alexander P. Mangerel
Comments: 39 pages; added Theorems 1.2 and 1.4, updated references and fixed a few typos
Subjects: Number Theory (math.NT)
[162]  arXiv:2108.11495 [pdf, ps, other]
Title: Binary Signed-Digit Integers and the Stern Diatomic Sequence
Authors: Laura Monroe
Comments: 13 pages, 0 figures. Portions of this previously appeared as arXiv:2103.05810 which was split for publication. To appear in Designs, Codes and Cryptography
Journal-ref: Des. Codes Cryptogr. 89 (2021) 1-10
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[163]  arXiv:2108.11555 [pdf, ps, other]
Title: On a local-global principle for quadratic twists of abelian varieties
Authors: Francesc Fité
Comments: 21 pages. Version to appear in Math. Ann. Some details and background material from v1 have been omitted
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[164]  arXiv:2108.11828 [pdf, other]
Title: Fourier non-uniqueness sets from totally real number fields
Authors: Danylo Radchenko, Martin Stoller
Comments: 29 pages, 2 figures; minor changes in the introduction; to appear in Commentarii Mathematici Helvetici
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
[165]  arXiv:2108.11937 [pdf, ps, other]
Title: Multiplicative functions with sum zero
Authors: Ammar Ali Neamah
Subjects: Number Theory (math.NT)
[166]  arXiv:2108.12283 [pdf, ps, other]
Title: On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case
Authors: Olga Balkanova, Dmitry Frolenkov, Han Wu
Subjects: Number Theory (math.NT)
[167]  arXiv:2108.12351 [pdf, ps, other]
Title: Additive functions in short intervals, gaps and a conjecture of Erdős
Authors: Alexander P. Mangerel
Comments: 36 pages
Subjects: Number Theory (math.NT)
[168]  arXiv:2108.12405 [pdf, ps, other]
Title: Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties
Authors: Fabrizio Barroero, Lars Kühne, Harry Schmidt
Comments: Comments are welcome
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[169]  arXiv:2108.12417 [pdf, other]
Title: Binary Signed-Digit Integers and the Stern Polynomial
Authors: Laura Monroe
Comments: 21 pages, 3 figures. Portions of this previously appeared as arXiv:2103.05810 which was split for publication
Subjects: Number Theory (math.NT)
[170]  arXiv:2108.12520 [pdf, ps, other]
Title: Sign changes of cusp form coefficients on indices that are sums of two squares
Authors: David Lowry-Duda
Comments: 14 pages
Subjects: Number Theory (math.NT)
[171]  arXiv:2108.12543 [pdf, ps, other]
Title: Integral representations for local dilogarithm and trilogarithm functions
Authors: Masato Kobayashi
Comments: 21 pages. This is the second version
Subjects: Number Theory (math.NT)
[172]  arXiv:2108.12577 [pdf, ps, other]
Title: Generic Newton polygons for $L$-functions of $(A,B)$-exponential sums
Authors: Liping Yang, Hao Zhang
Comments: 16 pages
Subjects: Number Theory (math.NT)
[173]  arXiv:2108.12656 [pdf, ps, other]
Title: Exceptional cases of adelic surjectivity for Drinfeld modules of rank 2
Authors: Chien-Hua Chen
Subjects: Number Theory (math.NT)
[174]  arXiv:2108.12660 [src]
Title: An explicit bound on reducibility of mod $\mathfrak{l}$ Galois image for Drinfeld modules of arbitrary rank and its application on the uniformity problem
Authors: Chien-Hua Chen
Comments: The proof of Proposition 3.1 is wrong, which makes Main Theorem 1 groundless
Subjects: Number Theory (math.NT)
[175]  arXiv:2108.12679 [pdf, ps, other]
Title: Congruences for Hasse--Witt matrices and solutions of $p$-adic KZ equations
Authors: Alexander Varchenko, Wadim Zudilin
Comments: Latex, 25 pages; v.2: appendix shortened and moved to Section 6
Subjects: Number Theory (math.NT); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Classical Analysis and ODEs (math.CA)
[176]  arXiv:2108.12733 [pdf, ps, other]
Title: A note on the Voronoi congruences and the residue of the Fermat quotient
Authors: Claire I. Levaillant
Comments: 12 pages, 27 references
Subjects: Number Theory (math.NT)
[177]  arXiv:2108.12796 [pdf, ps, other]
Title: $q$-Analogues of $π$-Related Formulae from Jackson's $_8φ_7$-Series via Inversion Approach
Authors: Xiaojing Chen, Wenchang Chu
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[178]  arXiv:2108.12979 [pdf, ps, other]
Title: Infinite families of crank functions, Stanton-type conjectures, and unimodality
Authors: Kathrin Bringmann, Kevin Gomez, Larry Rolen, Zack Tripp
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[179]  arXiv:2108.13116 [pdf, ps, other]
Title: Lower bounds for moments of the derivative of the Riemann zeta function
Authors: Peng Gao
Comments: 9 pages
Subjects: Number Theory (math.NT)
[180]  arXiv:2108.13132 [pdf, ps, other]
Title: The ternary Goldbach problem with a prime with a missing digit and primes of special types
Authors: Helmut Maier, Michael Th. Rassias
Comments: arXiv admin note: text overlap with arXiv:2006.07873
Subjects: Number Theory (math.NT)
[181]  arXiv:2108.13135 [pdf, ps, other]
Title: Derived deformation rings allowing congruences]{Derived deformation rings allowing congruences
Authors: Yichang Cai
Subjects: Number Theory (math.NT)
[182]  arXiv:2108.13146 [src]
Title: Additive energy of cyclic matrix groups and character sums with matrix exponential functions
Authors: Alina Ostafe, Igor E. Shparlinski
Comments: The submission is superseded by arXiv:2110.10941
Subjects: Number Theory (math.NT)
[183]  arXiv:2108.13173 [pdf, ps, other]
Title: Linear Recurrences of Order at Most Two in Small Divisors
Authors: A. Anas Chentouf
Subjects: Number Theory (math.NT)
[184]  arXiv:2108.13198 [pdf, ps, other]
Title: Local Maaß forms and Eichler--Selberg type relations for negative weight vector-valued mock modular forms
Authors: Joshua Males, Andreas Mono
Comments: 20 pages, no figures, comments welcome. Corrected an error in Proposition 4.1
Journal-ref: Pacific J. Math. 322 (2023) 381-406
Subjects: Number Theory (math.NT)
[185]  arXiv:2108.13199 [pdf, ps, other]
Title: Asymptotics of probability characteristics of additive arithmetic functions
Authors: Victor Volfson
Comments: 12 pages
Subjects: Number Theory (math.NT)
[186]  arXiv:2108.13204 [pdf, ps, other]
Title: On variants of the Euler sums and symmetric extensions of the Kaneko-Tsumura conjecture
Authors: Weiping Wang, Ce Xu
Subjects: Number Theory (math.NT)
[187]  arXiv:2108.13287 [pdf, other]
Title: On the rational approximation to Thue--Morse rational numbers
Authors: Yann Bugeaud, Guo-Niu Han
Subjects: Number Theory (math.NT)
[188]  arXiv:2108.13397 [pdf, other]
Title: On the birational section conjecture with strong birationality assumptions
Authors: Giulio Bresciani
Comments: Final version
Journal-ref: Inventiones mathematicae (2023)
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[189]  arXiv:2108.13441 [pdf, ps, other]
Title: On Integers Whose Sum is the Reverse of their Product
Authors: Xander Faber, Jon Grantham
Comments: 15 pages; 4 figures; added additional references to the literature and a new section; Python experimentation/visualization code available at this https URL
Subjects: Number Theory (math.NT); Formal Languages and Automata Theory (cs.FL)
[190]  arXiv:2108.13470 [pdf, ps, other]
Title: Class field towers and minimal models
Authors: Igor Nikolaev
Comments: 8 pages. arXiv admin note: text overlap with arXiv:2012.08237
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Operator Algebras (math.OA)
[191]  arXiv:2108.13471 [pdf, other]
Title: On the 2-adic valuation of (a^b-c^d)
Authors: Luca Onnis
Comments: 15 pages, 9 figures
Subjects: Number Theory (math.NT)
[192]  arXiv:2108.13480 [pdf, ps, other]
Title: Arithmetic statistics for Galois deformation rings
Authors: Anwesh Ray, Tom Weston
Comments: Version 2: Minor corrections, accepted for publication in the Ramanujan J
Subjects: Number Theory (math.NT)
[193]  arXiv:2108.13532 [pdf, ps, other]
Title: On the regularized $L^4$-norm for Eisenstein series in the level aspect, Part II
Authors: Jiakun Pan
Subjects: Number Theory (math.NT)
[194]  arXiv:2108.13546 [pdf, ps, other]
Title: Extended genus field of cyclic Kummer extensions of rational function fields
Authors: Edgar Omar Curiel-Anaya, Myriam Rosalía Maldonado-Ramírez, Martha Rzedowski-Calderón
Comments: 13 pages
Subjects: Number Theory (math.NT)
[195]  arXiv:2108.13625 [pdf, other]
Title: Tamagawa Products for Elliptic Curves Over Number Fields
Authors: Yunseo Choi, Sean Li, Apoorva Panidapu, Casia Siegel
Comments: 40 pages, 9 figures, 17 tables
Subjects: Number Theory (math.NT)
[196]  arXiv:2108.13845 [pdf, ps, other]
Title: On a general Syracuse problem with conjectures
Authors: Abderrahman Bouhamidi
Comments: 18 pages
Subjects: Number Theory (math.NT)
[197]  arXiv:2108.13868 [pdf, ps, other]
Title: Sharp bound for the fourth moment of holomorphic Hecke cusp forms
Authors: Peter Zenz
Comments: 28 pages
Subjects: Number Theory (math.NT)
[198]  arXiv:2108.13879 [pdf, ps, other]
Title: Companion points on the eigenvariety with non-regular weights
Authors: Zhixiang Wu
Comments: 15 pages
Subjects: Number Theory (math.NT)
[199]  arXiv:2108.13991 [pdf, ps, other]
Title: A Class of Identities Associated with Dirichlet Series Satisfying Hecke's Functional Equation
Authors: Bruce C. Berndt, Atul Dixit, Rajat Gupta, Alexandru Zaharescu
Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
[200]  arXiv:2108.00130 (cross-list from math.CV) [pdf, ps, other]
Title: Solution of Mumford's second problem
Authors: Julia Bernatska, Yaacov Kopeliovich
Comments: 12 pages
Subjects: Complex Variables (math.CV); Number Theory (math.NT)
[201]  arXiv:2108.01008 (cross-list from math.DS) [pdf, ps, other]
Title: Bernoulli convolutions with Garsia parameters in $(1,\sqrt{2}]$ have continuous density functions
Authors: Han Yu
Comments: Version accepted in Proc. Am. Math. Soc
Subjects: Dynamical Systems (math.DS); Number Theory (math.NT)
[202]  arXiv:2108.02022 (cross-list from math.CO) [pdf, ps, other]
Title: The Jacobian of Cyclic Voltage Covers of $K_n$
Authors: Sophia Gonet
Comments: 27 pages
Subjects: Combinatorics (math.CO); Number Theory (math.NT)
[203]  arXiv:2108.02845 (cross-list from math.AG) [pdf, ps, other]
Title: A log-motivic cohomology for semistable varieties and its $p$-adic deformation theory
Authors: Oliver Gregory, Andreas Langer
Comments: 33 pages
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[204]  arXiv:2108.03017 (cross-list from math.RT) [pdf, ps, other]
Title: Local distinction, quadratic base change and automorphic induction for $\mathrm{GL_n}$
Authors: Nadir Matringe
Comments: A discussion on the parity of the Artin conductor of symplectic representations has been added. Final version to appear in Journal de Th\'eorie des Nombres de Bordeauxx
Subjects: Representation Theory (math.RT); Number Theory (math.NT)
[205]  arXiv:2108.03079 (cross-list from math.AT) [pdf, ps, other]
Title: Strictly Commutative Complex Orientations of $Tmf_1(N)$
Authors: Dominik Absmeier
Subjects: Algebraic Topology (math.AT); Number Theory (math.NT)
[206]  arXiv:2108.03088 (cross-list from cs.IT) [pdf, ps, other]
Title: The Differential Spectrum of the Power Mapping $x^{p^n-3}$
Authors: Haode Yan, Yongbo Xia, Chunlei Li, Tor Helleseth, Maosheng Xiong, Jinquan Luo
Subjects: Information Theory (cs.IT); Number Theory (math.NT)
[207]  arXiv:2108.03565 (cross-list from math.RT) [pdf, ps, other]
Title: Certain Fourier Operators on $\mathrm{GL}_1$ and Local Langlands Gamma functions
Authors: Dihua Jiang, Zhilin Luo
Comments: Correct a mistake in Proposition 4.3. Comments welcome
Journal-ref: Pacific J. Math. 318 (2022) 339-374
Subjects: Representation Theory (math.RT); Number Theory (math.NT)
[208]  arXiv:2108.03566 (cross-list from math.RT) [pdf, ps, other]
Title: Certain Fourier Operators and their Associated Poisson Summation Formulae on $\mathrm{GL}_1$
Authors: Dihua Jiang, Zhilin Luo
Comments: Comments are welcome
Journal-ref: Pacific J. Math. 326 (2023) 301-372
Subjects: Representation Theory (math.RT); Number Theory (math.NT)
[209]  arXiv:2108.03832 (cross-list from math.AG) [pdf, ps, other]
Title: On log minimality of weak K-moduli compactifications of Calabi-Yau varieties
Authors: Yuji Odaka
Comments: 23 pages
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG); Number Theory (math.NT)
[210]  arXiv:2108.04132 (cross-list from math.LO) [pdf, ps, other]
Title: Decidability of positive characteristic tame Hahn fields in $\mathcal{L}_t$
Authors: Victor Lisinski
Comments: Clarifications to fill gaps in some proofs
Subjects: Logic (math.LO); Number Theory (math.NT)
[211]  arXiv:2108.04147 (cross-list from math.CA) [pdf, ps, other]
Title: Discrete multilinear maximal functions and number theory
Authors: Theresa C. Anderson
Comments: To appear in Illinois Journal of Math
Subjects: Classical Analysis and ODEs (math.CA); Number Theory (math.NT)
[212]  arXiv:2108.04148 (cross-list from math.CO) [pdf, ps, other]
Title: Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product
Authors: Liuquan Wang
Comments: 11 pages
Subjects: Combinatorics (math.CO); Number Theory (math.NT)
[213]  arXiv:2108.04163 (cross-list from math.AG) [pdf, ps, other]
Title: Steinberg symbols and reciprocity sheaves
Authors: Junnosuke Koizumi
Comments: 28 pages, 4 figures, to appear in Ann. K-Theory
Journal-ref: Ann. K-Th. 7 (2022) 695-730
Subjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT); Number Theory (math.NT)
[214]  arXiv:2108.04363 (cross-list from math.CO) [pdf, ps, other]
Title: Reciprocity between partitions and compositions
Authors: George Beck, Shane Chern
Subjects: Combinatorics (math.CO); Number Theory (math.NT)
[215]  arXiv:2108.04513 (cross-list from math.AC) [pdf, ps, other]
Title: Inverse polynomials of numerical semigroup rings
Authors: Kazufumi Eto, Kei-ichi Watanabe
Subjects: Commutative Algebra (math.AC); Number Theory (math.NT)
[216]  arXiv:2108.04538 (cross-list from math.GR) [pdf, ps, other]
Title: Fractional weight multiplier systems on SU(d,1)
Authors: Richard M. Hill
Subjects: Group Theory (math.GR); Number Theory (math.NT)
[217]  arXiv:2108.04807 (cross-list from math.CV) [pdf, ps, other]
Title: Zero-free regions near a line
Authors: Kelly Bickel, J.E. Pascoe, Meredith Sargent
Comments: 24 pages
Subjects: Complex Variables (math.CV); Functional Analysis (math.FA); Number Theory (math.NT)
[218]  arXiv:2108.05886 (cross-list from math.CO) [pdf, ps, other]
Title: Geometry of the minimal solutions of a linear Diophantine Equation
Authors: Papa Amar Sissokho
Comments: 12 pages; To appear in SIAM J. Discrete Math
Subjects: Combinatorics (math.CO); Commutative Algebra (math.AC); Number Theory (math.NT)
[219]  arXiv:2108.06253 (cross-list from math.CO) [pdf, ps, other]
Title: The typical approximate structure of sets with bounded sumset
Authors: Marcelo Campos, Matthew Coulson, Oriol Serra, Maximilian Wötzel
Comments: a) Replaced Theorem 2.2 with a less general statement (proof of previously claimed result contained an error), no influence on the main results of this article. b) Incorporated numerous suggestions by anonymous referees to improve presentation, thank you!
Subjects: Combinatorics (math.CO); Number Theory (math.NT); Probability (math.PR)
[220]  arXiv:2108.06775 (cross-list from math.CO) [pdf, ps, other]
Title: Limits of Jensen polynomials for partitions and other sequences
Authors: Cormac O'Sullivan
Comments: 20 pages, 1 figure
Subjects: Combinatorics (math.CO); Number Theory (math.NT)
[221]  arXiv:2108.06780 (cross-list from math.DS) [pdf, other]
Title: Dynamics of Ostrowski skew-product: I. Limit laws and Hausdorff dimensions
Authors: Valérie Berthé, Jungwon Lee
Comments: 36 pages
Subjects: Dynamical Systems (math.DS); Number Theory (math.NT)
[222]  arXiv:2108.07185 (cross-list from math.AG) [pdf, ps, other]
Title: The Scheme of Monogenic Generators I: Representability
Authors: Sarah Arpin, Sebastian Bozlee, Leo Herr, Hanson Smith
Comments: 32 pages, comments welcome; Version 1 has been split into two papers. This is the first of the two papers
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[223]  arXiv:2108.07318 (cross-list from cs.IT) [pdf, ps, other]
Title: Peak Sidelobe Level and Peak Crosscorrelation of Golay-Rudin-Shapiro Sequences
Authors: Daniel J. Katz, Courtney M. van der Linden
Comments: 39 pages
Subjects: Information Theory (cs.IT); Discrete Mathematics (cs.DM); Signal Processing (eess.SP); Combinatorics (math.CO); Number Theory (math.NT)
[224]  arXiv:2108.07459 (cross-list from math.AG) [pdf, other]
Title: Trace formalism for motivic cohomology
Authors: Tomoyuki Abe
Journal-ref: Épijournal de Géométrie Algébrique, Volume 7 (March 19, 2023) epiga:9742
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[225]  arXiv:2108.09421 (cross-list from math.CV) [pdf, ps, other]
Title: Mellin-Barnes and the method of brackets
Authors: Ivan Gonzalez, Igor Kondrashuk, Victor H. Moll, Luis M. Recabarren
Subjects: Complex Variables (math.CV); High Energy Physics - Phenomenology (hep-ph); Mathematical Physics (math-ph); Number Theory (math.NT)
[226]  arXiv:2108.10253 (cross-list from math.AG) [pdf, other]
Title: Irregular cusps of ball quotients
Authors: Yota Maeda
Comments: 24 pages
Journal-ref: Math. Nachr. (2023), 1-29
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[227]  arXiv:2108.10777 (cross-list from math.AG) [pdf, other]
Title: Dynamical moduli spaces and polynomial endomorphisms of configurations
Authors: Talia Blum, John R. Doyle, Trevor Hyde, Colby Kelln, Henry Talbott, Max Weinreich
Comments: 26 pages, comments welcome!
Journal-ref: Arnold Math. J. 8 (2022) 285-317
Subjects: Algebraic Geometry (math.AG); Dynamical Systems (math.DS); Number Theory (math.NT)
[228]  arXiv:2108.11313 (cross-list from math.CO) [pdf, ps, other]
Title: On the extremal values of the cyclic continuants of Motzkin and Straus
Authors: Alessandro De Luca (1), Luca Q. Zamboni (2) ((1) DIETI, Università di Napoli Federico II, Italy, (2) Institut Camille Jordan, CNRS UMR 5208, Université Lyon 1, France)
Comments: Preliminary version, 21 pages
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM); Number Theory (math.NT)
[229]  arXiv:2108.11322 (cross-list from math.RA) [pdf, ps, other]
Title: On $\mathbb{Z}_N\rtimes\mathbb{Z}_2$-Hopf-Galois structures
Authors: Namrata Arvind, Saikat Panja
Subjects: Rings and Algebras (math.RA); Group Theory (math.GR); Number Theory (math.NT)
[230]  arXiv:2108.11595 (cross-list from math.AG) [pdf, ps, other]
Title: Potential density of projective varieties having an int-amplified endomorphism
Authors: Jia Jia, Takahiro Shibata, De-Qi Zhang
Comments: 12 pages; comments are welcome!
Journal-ref: New York Journal of Mathematics, Volume 28, February 2022, 433-444
Subjects: Algebraic Geometry (math.AG); Dynamical Systems (math.DS); Number Theory (math.NT)
[231]  arXiv:2108.11862 (cross-list from math.AG) [pdf, ps, other]
Title: Chow dilogarithm and strong Suslin reciprocity law
Authors: Vasily Bolbachan
Comments: The final version
Subjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT); Number Theory (math.NT)
[232]  arXiv:2108.12254 (cross-list from math.GR) [pdf, ps, other]
Title: Bounded generation by root elements for Chevalley groups defined over rings of integers of function fields with an application in strong boundedness
Authors: Alexander A. Trost
Comments: 27 pages
Subjects: Group Theory (math.GR); Number Theory (math.NT)
[233]  arXiv:2108.12404 (cross-list from math.AG) [pdf, ps, other]
Title: Residual finiteness for central extensions of lattices in $\mathrm{PU}(n,1)$ and negatively curved projective varieties
Authors: Matthew Stover, Domingo Toledo
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG); Group Theory (math.GR); Geometric Topology (math.GT); Number Theory (math.NT)
[234]  arXiv:2108.12785 (cross-list from math.AG) [pdf, ps, other]
Title: On the cohomology of p-adic analytic spaces, II: The $C_{\rm st}$-conjecture
Authors: Pierre Colmez, Wiesława Nizioł
Comments: Shortened version: Chapter 7 removed (and will appear elsewhere)
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[235]  arXiv:2108.13402 (cross-list from math.AG) [pdf, ps, other]
Title: Explicit equations of 800 conics on a Barth-Bauer quartic
Authors: Bartosz Naskręcki
Comments: 12 pages, 4 figures, 3 appendices; ancillary Magma files
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[236]  arXiv:2108.06457 (cross-list from cs.CR) [pdf, other]
Title: Probability Distributions for Elliptic Curves in the CGL Hash Function
Authors: Dhruv Bhatia, Kara Fagerstrom, Maximillian Watson
Comments: 34 pages, 15 figures. Written during the 2021 Rose Hulman Institute of Technology Mathematics REU
Subjects: Cryptography and Security (cs.CR); Number Theory (math.NT)
[237]  arXiv:2108.13903 (cross-list from hep-th) [pdf, other]
Title: Mahler Measure for a Quiver Symphony
Authors: Jiakang Bao, Yang-Hui He, Ali Zahabi
Comments: 52 pages; v2: minor corrections and references added
Journal-ref: Commun. Math. Phys. 394, 573-624 (2022)
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Number Theory (math.NT)
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