Number Theory

Authors and titles for math.NT in May 2024

[1]  arXiv:2405.00270 [pdf, ps, other]

Title: Base change and Iwasawa Main Conjectures for ${\rm GL}_2$

Authors: Ashay Burungale, Francesc Castella, Christopher Skinner

Subjects: Number Theory (math.NT)

[2]  arXiv:2405.00274 [pdf, ps, other]

Title: Large Values of Newform Dedekind Sums

Authors: Georgia Corbett, Matthew P. Young

Comments: 9 pages

Subjects: Number Theory (math.NT)

[3]  arXiv:2405.00544 [pdf, ps, other]

Title: Large sums of high order characters II

Authors: Alexander P. Mangerel, Yichen You

Comments: 32 pages, comments welcome

Subjects: Number Theory (math.NT)

[4]  arXiv:2405.00658 [pdf, ps, other]

Title: A Note on Large Sums of Divisor-Bounded Multiplicative Functions

Authors: Claire Frechette, Mathilde Gerbelli-Gauthier, Alia Hamieh, Naomi Tanabe

Comments: 16 pages, project begun at Women in Numbers 6

Subjects: Number Theory (math.NT)

[5]  arXiv:2405.00868 [pdf, ps, other]

Title: The Furstenberg-Sárközy theorem for polynomials in one or more prime variables

Authors: John R. Doyle, Alex Rice

Comments: 22 pages. arXiv admin note: text overlap with arXiv:2006.15400

Subjects: Number Theory (math.NT); Combinatorics (math.CO)

[6]  arXiv:2405.00996 [pdf, ps, other]

Title: Joint value distribution of Hecke--Maass forms

Authors: Shenghao Hua, Bingrong Huang, Liangxun Li

Comments: 22 pages. Comments welcome

Subjects: Number Theory (math.NT)

[7]  arXiv:2405.01056 [pdf, ps, other]

Title: Large Sieve Inequalities for periods of Maass forms

Authors: Dimitrios Lekkas, Marios Voskou

Comments: 20 pages, comments welcome!

Subjects: Number Theory (math.NT)

[8]  arXiv:2405.01184 [pdf, other]

Title: On the Zeros of the Miller Basis of Cusp Forms

Authors: Roei Raveh

Subjects: Number Theory (math.NT)

[9]  arXiv:2405.01219 [pdf, ps, other]

Title: Special values of Green's functions on hyperbolic $3$-space

Authors: Sebastián Herrero, Özlem Imamoglu, Anna-Maria von Pippich, Markus Schwagenscheidt

Subjects: Number Theory (math.NT)

[10]  arXiv:2405.01278 [pdf, ps, other]

Title: Generalized cyclotomic polynomials associated with regular systems of divisors and arbitrary sets of positive integers

Authors: László Tóth

Comments: 20 pages

Subjects: Number Theory (math.NT)

[11]  arXiv:2405.01414 [pdf, ps, other]

Title: Mass equidistribution for Poincaré series of large index

Authors: Noam Kimmel

Subjects: Number Theory (math.NT)

[12]  arXiv:2405.01426 [pdf, other]

Title: Co-rank $1$ Arithmetic Siegel--Weil I: Local non-Archimedean

Authors: Ryan C. Chen

Comments: 111 pages

Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Representation Theory (math.RT)

[13]  arXiv:2405.01427 [pdf, other]

Title: Co-rank $1$ Arithmetic Siegel--Weil II: Local Archimedean

Authors: Ryan C. Chen

Comments: 29 pages

Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Representation Theory (math.RT)

[14]  arXiv:2405.01428 [pdf, other]

Title: Co-rank $1$ Arithmetic Siegel--Weil III: Geometric local-to-global

Authors: Ryan C. Chen

Comments: 67 pages

Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Representation Theory (math.RT)

[15]  arXiv:2405.01429 [pdf, other]

Title: Co-rank $1$ Arithmetic Siegel--Weil IV: Analytic local-to-global

Authors: Ryan C. Chen

Comments: 69 pages

Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Representation Theory (math.RT)

[16]  arXiv:2405.01512 [pdf, ps, other]

Title: Euler Products at the Centre and Applications to Chebyshev's Bias

Authors: Arshay Sheth

Comments: 17 pages, comments welcome!

Subjects: Number Theory (math.NT)

[17]  arXiv:2405.01530 [pdf, ps, other]

Title: Representation functions with prescribed rates of growth

Authors: Christian Táfula

Comments: 23 pages

Subjects: Number Theory (math.NT); Combinatorics (math.CO)

[18]  arXiv:2405.01877 [pdf, ps, other]

Title: A divisor generating q-series identity and its applications to probability theory and random graphs

Authors: Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni, Bibekananda Maji

Comments: 33 pages, comments are welcome!

Subjects: Number Theory (math.NT); Combinatorics (math.CO); Probability (math.PR)

[19]  arXiv:2405.01953 [pdf, ps, other]

Title: Mahler equations for Zeckendorf numeration

Authors: Olivier Carton, Reem Yassawi

Comments: 33 pages, 6 figures

Subjects: Number Theory (math.NT); Formal Languages and Automata Theory (cs.FL)

[20]  arXiv:2405.02112 [pdf, ps, other]

Title: On a generalization of R. Chapman's "evil determinant"

Authors: Li-Yuan Wang, Hai-Liang Wu, He-Xia Ni

Subjects: Number Theory (math.NT)

[21]  arXiv:2405.02174 [pdf, ps, other]

Title: Hausdorff dimension of the exceptional set of the law of large numbers in Pierce expansions

Authors: Min Woong Ahn

Comments: 15 pages

Subjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)

[22]  arXiv:2405.02419 [pdf, ps, other]

Title: On quotients of derivatives of $L$-functions inside the critical strip

Authors: Rashi Lunia

Journal-ref: Journal of Number Theory, vol. 259, 2024, pp. 16-37

Subjects: Number Theory (math.NT)

[23]  arXiv:2405.02428 [pdf, ps, other]

Title: Extreme values of $L$-functions of newforms

Authors: Sanoli Gun, Rashi Lunia

Journal-ref: Bulletin of the London Mathematical Society, vol. 56, 2024, 1570-1586

Subjects: Number Theory (math.NT)

[24]  arXiv:2405.02443 [pdf, ps, other]

Title: On extreme values of quadratic twists of Dirichlet-type $L$-functions

Authors: Sanoli Gun, Rashi Lunia

Subjects: Number Theory (math.NT)

[25]  arXiv:2405.02651 [pdf, ps, other]

Title: Mind the (multiplicative) gaps

Authors: Emmanuel Kowalski

Comments: 19 pages; not currently intended for publication

Subjects: Number Theory (math.NT)