Number Theory

Authors and titles for May 2018

[1] arXiv:1805.00072 [pdf, other]

Title: On p-adic Multidimensional Continued Fractions

Nadir Murru, Lea Terracini

Subjects: Number Theory (math.NT)

[2] arXiv:1805.00075 [pdf, other]

Title: Greedy approximations by signed harmonic sums and the Thue--Morse sequence

Sandro Bettin, Giuseppe Molteni, Carlo Sanna

Comments: 30 pages, 5 figures

Journal-ref: Advances in Mathematics, Volume 366, 3 June 2020, 107068

Subjects: Number Theory (math.NT)

[3] arXiv:1805.00093 [pdf, other]

Title: A new perspective on the powers of two descent for discrete logarithms in finite fields

Thorsten Kleinjung, Benjamin Wesolowski

Comments: ANTS-XIII, Thirteenth Algorithmic Number Theory Symposium

Journal-ref: Open Book Series 2 (2019) 343-352

Subjects: Number Theory (math.NT)

[4] arXiv:1805.00131 [pdf, other]

Title: Wieferich Primes and a mod $p$ Leopoldt Conjecture

Gebhard Boeckle, David-A. Guiraud, Sudesh Kalyanswamy, Chandrashekhar Khare

Comments: 31 pages, 5 tables

Subjects: Number Theory (math.NT)

[5] arXiv:1805.00209 [pdf, other]

Title: Quantitative non-vanishing of central values of certain $L$-functions on ${\rm GL}(2)\times {\rm GL}(3)$

Shingo Sugiyama, Masao Tsuzuki

Comments: Some typos are fixed. Theorem 1.4, Lemma 3.2 and Proposition 3.3 are corrected

Journal-ref: Math. Z., 301 (2022), 1447--1479

Subjects: Number Theory (math.NT)

[6] arXiv:1805.00230 [pdf, other]

Title: Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms

Surjeet Kaushik, Narasimha Kumar

Comments: Submitted for publication

Journal-ref: Arch. Math. 112, 241 to 248 (2019)

Subjects: Number Theory (math.NT)

[7] arXiv:1805.00244 [pdf, other]

Title: Inverse Satake isomorphism and change of weight

Noriyuki Abe, Florian Herzig, Marie-France Vignéras

Comments: 60 pages

Journal-ref: Represent. Theory 26 (2022), 264-324

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

[8] arXiv:1805.00392 [pdf, other]

Title: Derived Hecke algebra and automorphic L-invariants

Lennart Gehrmann

Comments: 16 pages, details added, to appear in Trans. Amer. Math. Soc

Subjects: Number Theory (math.NT)

[9] arXiv:1805.00522 [pdf, other]

Title: Tate Duality In Positive Dimension Over Function Fields

Zev Rosengarten

Comments: 245 pages

Subjects: Number Theory (math.NT)

[10] arXiv:1805.00544 [pdf, other]

Title: A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds

Wadim Zudilin

Journal-ref: SIGMA 14 (2018), 086, 16 pages

Subjects: Number Theory (math.NT); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Classical Analysis and ODEs (math.CA); K-Theory and Homology (math.KT)

[11] arXiv:1805.00633 [pdf, other]

Title: Counting cusp forms by analytic conductor

Farrell Brumley, Djordje Milićević

Comments: 103 pages, 5 figures, to appear in Annales Scientifiques de l'École Normale Supérieure

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

[12] arXiv:1805.00639 [pdf, other]

Title: Infinitely many elliptic curves of rank exactly two, II

Keunyoung Jeong

Comments: 8 pages

Subjects: Number Theory (math.NT)

[13] arXiv:1805.00724 [pdf, other]

Title: Value-distribution of cubic Hecke $L$-functions

Amir Akbary, Alia Hamieh

Subjects: Number Theory (math.NT)

[14] arXiv:1805.00750 [pdf, other]

Title: Hermite-Thue equation: Pad\'e approximations and Siegel's lemma

Tapani Matala-aho, Louna Seppälä

Comments: 3 tables

Subjects: Number Theory (math.NT)

[15] arXiv:1805.00865 [pdf, other]

Title: Sums of reciprocals of fractional parts

Reynold Fregoli

Subjects: Number Theory (math.NT)

[16] arXiv:1805.00974 [pdf, other]

Title: Adelic Voronoi Summation and Subconvexity for GL(2) L-Functions in the depth Aspect

Edgar Assing

Comments: 30 pages, v2: new title and improved exposition

Subjects: Number Theory (math.NT)

[17] arXiv:1805.00995 [pdf, other]

Title: The $p$-adic Analysis of Stirling Numbers via Higher Order Bernoulli Numbers

Arnold Adelberg

Comments: 22 pages, under consideration by the International Journal of Number Theory. A new unified method of studying Stirling numbers of both kinds is developed. and classical theorems for the prime $2$ have new, simpler proofs. The results are generalized to arbitrary primes, with essentially the same proofs

Subjects: Number Theory (math.NT)

[18] arXiv:1805.01103 [pdf, other]

Title: Computer-Assisted Proofs of Congruences for Multipartitions and Divisor Function Convolutions, based on Methods of Differential Algebra

Alexandru Pascadi

Comments: 25 pages, 1 figure, 2 tables; 6 ancillary files containing program code in MAPLE and C++

Journal-ref: Ramanujan J. 57 (2022): 1-36

Subjects: Number Theory (math.NT)

[19] arXiv:1805.01119 [pdf, other]

Title: A note on entire $L$-functions

Andrés Chirre

Comments: 18 pages. To appear in Bulletin of the Brazilian Mathematical Society

Subjects: Number Theory (math.NT)

[20] arXiv:1805.01121 [pdf, other]

Title: On a theta product of Jacobi and its applications to $q$-gamma products

Mohamed El Bachraoui, József Sándor

Comments: 13 pages, published in J. Math. Anal. Appl

Subjects: Number Theory (math.NT)

[21] arXiv:1805.01196 [pdf, other]

Title: Strongly perfect lattices sandwiched between Barnes-Wall lattices

Sihuang Hu, Gabriele Nebe

Journal-ref: J. London Math. Soc. 101 (2020), 1068-1089

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

[22] arXiv:1805.01254 [pdf, other]

Title: q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon

Ofir Gorodetsky

Comments: Incorporated comments from referees. Accepted for publication in Int. J. Number Theory

Journal-ref: Int. J. Number Theory 15 (2019), no. 9, 1919-1968

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

[23] arXiv:1805.01400 [pdf, other]

Title: Simple supercuspidal L-packets of quasi-split classical groups

Masao Oi

Comments: 147 pages, revised according to the referee's suggestions, to appear in Mem. Amer. Math. Soc

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

[24] arXiv:1805.01429 [pdf, other]

Title: Quadratic Irrationals, Closed Geodesics on the Modular Surface and Dynamical Zeta Functions

Peter Hazard

Comments: 25 pages

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

[25] arXiv:1805.01504 [pdf, other]

Title: Weighted lattice point sums in lattice polytopes, unifying Dehn--Sommerville and Ehrhart--Macdonald

Matthias Beck, Paul E. Gunnells, Evgeny Materov

Comments: 19 pages, three figures; replaced old (and, so we thought, cool) title "The Bott-Brion-Dehn-Ehrhart-Euler-Khovanskii-Maclaurin-Puhklikov-Sommerville-Vergne formula for simple lattice polytopes" and corrected typos; to appear in Discrete & Computational Geometry

Journal-ref: Discrete & Computational Geometry 65, no. 2 (2021), 365-384

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

[26] arXiv:1805.01508 [pdf, other]

Title: First Moment of Distances Between Centres of Ford Spheres

Kayleigh Measures

Comments: 28 pages, 6 figures

Subjects: Number Theory (math.NT)

[27] arXiv:1805.01622 [pdf, other]

Title: La constante de Manin et le degr\'e modulaire d'une courbe elliptique

Karim Belabas, Dominique Bernardi, Bernadette Perrin-Riou

Comments: 20 pages, in French

Subjects: Number Theory (math.NT)

[28] arXiv:1805.01666 [pdf, other]

Title: A reformulation of the Siegel series and intersection numbers

Sungmun Cho, Takuya Yamauchi

Comments: 52 pages

Subjects: Number Theory (math.NT)

[29] arXiv:1805.01885 [pdf, other]

Title: Sequential periods of the crystalline Frobenius

Julian Rosen

Comments: 24 pages, comments are very welcome

Subjects: Number Theory (math.NT)

[30] arXiv:1805.01998 [pdf, other]

Title: A generalization of the Goresky-Klapper conjecture, Part I

Badria Alsulmi, Todd Cochrane, Michael J. Mossinghoff, Vincent Pigno, Chris Pinner, C.J. Richardson, Ian Thompson

Subjects: Number Theory (math.NT)

[31] arXiv:1805.01999 [pdf, other]

Title: Some new inequalities for the $q$-gamma and related functions

Mohamed El Bachraoui, József Sándor

Comments: Submitted 23 January 2019, pages 17

Subjects: Number Theory (math.NT)

[32] arXiv:1805.02064 [pdf, other]

Title: Traces of CM values and cycle integrals of polyharmonic Maass forms

Toshiki Matsusaka

Comments: 23 pages, added Theorem 1.3 according to the first referees' comments. This is a pre-print of an article published in Research in Number Theory. The final authenticated version (after the second referee reports) will be available at DOI: https://doi.org/10.1007/s40993-018-0148-4

Subjects: Number Theory (math.NT)

[33] arXiv:1805.02071 [pdf, other]

Title: Central Values of $GL(2)\times GL(3)$ Rankin-Selberg $L$-functions with Applications

Qinghua Pi

Comments: 18 pages

Subjects: Number Theory (math.NT)

[34] arXiv:1805.02076 [pdf, other]

Title: On a method of evaluation of zeta-constants based on one number theoretic approach

Ekatherina A. Karatsuba

Subjects: Number Theory (math.NT)

[35] arXiv:1805.02112 [pdf, other]

Title: On primitive elements of algebraic function fields and models of $X_0(N)$

Iva Kodrnja, Goran Muić

Comments: arXiv admin note: text overlap with arXiv:1305.2428

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

[36] arXiv:1805.02126 [pdf, other]

Title: Motivic multiple zeta values reletive to \mu_2

Zhongyu Jin, Jiangtao Li

Comments: 27 pages

Subjects: Number Theory (math.NT)

[37] arXiv:1805.02225 [pdf, other]

Title: An Upper Bound for the Moments of a G.C.D. related to Lucas Sequences

Daniele Mastrostefano

Comments: 10 pages. The main result has been improved

Subjects: Number Theory (math.NT)

[38] arXiv:1805.02467 [pdf, other]

Title: Some supercongruences of arbitrary length

Frits Beukers, Eric Delaygue

Subjects: Number Theory (math.NT)

[39] arXiv:1805.02615 [pdf, other]

Title: A generalization of the Goresky-Klapper conjecture, Part II

Todd Cochrane, Michael J. Mossinghoff, Chris Pinner, C.J. Richardson

Subjects: Number Theory (math.NT)

[40] arXiv:1805.02756 [pdf, other]

Title: The power-saving Manin-Peyre's conjectures for a senary cubic

Sandro Bettin, Kevin Destagnol

Comments: 29 pages (title fixed)

Journal-ref: Mathematika 65 (2019) 789-830

Subjects: Number Theory (math.NT)

[41] arXiv:1805.02863 [pdf, other]

Title: Fields of definition of finite hypergeometric functions

Frits Beukers

Comments: 8 pages

Subjects: Number Theory (math.NT)

[42] arXiv:1805.02905 [pdf, other]

Title: Almost $C_p$ Galois representations and vector bundles

Jean-Marc Fontaine

Comments: 46 pages

Subjects: Number Theory (math.NT)

[43] arXiv:1805.02913 [pdf, other]

Title: Level curves of rational functions and unimodular points on rational curves

Fedor Pakovich, Igor E. Shparlinski

Subjects: Number Theory (math.NT)

[44] arXiv:1805.02945 [pdf, other]

Title: The number of solutions of the Erd\H{o}s-Straus Equation and sums of $k$ unit fractions

Christian Elsholtz, Stefan Planitzer

Subjects: Number Theory (math.NT)

[45] arXiv:1805.02978 [pdf, other]

Title: Bielliptic smooth plane curves and quadratic points

Eslam Badr, Francesc Bars

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

[46] arXiv:1805.03003 [pdf, other]

Title: On linear relations for Dirichlet series formed by recursive sequences of second order

Carsten Elsner, Niclas Technau

Subjects: Number Theory (math.NT)

[47] arXiv:1805.03029 [pdf, other]

Title: Some Order-Theoretic Properties of the Zeros of the Zeta Function

Boian Lazov

Comments: 3 pages

Subjects: Number Theory (math.NT)

[48] arXiv:1805.03038 [pdf, other]

Title: A sum of squares not divisible by a prime

Kyoungmin Kim, Byeong-Kweon Oh

Comments: 14 pages

Subjects: Number Theory (math.NT)

[49] arXiv:1805.03097 [pdf, other]

Title: Full Classification of permutation rational functions and complete rational functions of degree three over finite fields

Andrea Ferraguti, Giacomo Micheli

Comments: Using our results, we now also characterize complete permutation rational functions of degree 3

Subjects: Number Theory (math.NT); Cryptography and Security (cs.CR); Discrete Mathematics (cs.DM)

[50] arXiv:1805.03186 [pdf, other]

Title: New methods to find patches of invisible integer lattice points

Austin Goodrich, Aba Mbirika, Jasmine Nielsen

Comments: 31 pages, version 2 has substantial changes to improve exposition and visual presentation. Submitted to journal Involve

Journal-ref: Involve 14 (2021) 283-310

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