Number Theory

Authors and titles for math.NT in Aug 2021

[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)