Number Theory

Authors and titles for May 2018

[101] arXiv:1805.07105 [pdf, other]

Title: Irreducible polynomials over $\mathbb{F}_{2^r}$ with three prescribed coefficients

Ofir Gorodetsky

Comments: Incorporated referee comments. Accepted for publication in Finite Fields Appl

Journal-ref: Finite Fields Appl. 56 (2019), 150-187

Subjects: Number Theory (math.NT)

[102] arXiv:1805.07127 [pdf, other]

Title: On the generalized Fermat equation $a^2+3b^6=c^n$

Angelos Koutsianas

Comments: Minor modifications

Subjects: Number Theory (math.NT)

[103] arXiv:1805.07163 [pdf, other]

Title: The maximum size of short character sums

Marc Munsch

Subjects: Number Theory (math.NT)

[104] arXiv:1805.07167 [pdf, other]

Title: No singular modulus is a unit

Yu. Bilu, P. Habegger, L. Kühne

Comments: Dedicated to David Masser on the occasion of his 70th birthday. Version 2 has a new title, updated references, and contains minor corrections. 31 pages, to appear in IMRN. Link to scripts this https URL

Subjects: Number Theory (math.NT)

[105] arXiv:1805.07461 [pdf, other]

Title: The prime geodesic theorem in square mean

Antal Balog, András Biró, Gergely Harcos, Péter Maga

Comments: 7 pages, LaTeX2e

Journal-ref: J. Number Theory 198 (2019), 239-249

Subjects: Number Theory (math.NT)

[106] arXiv:1805.07530 [pdf, other]

Title: Shabat Polynomials and Monodromy Groups of Trees Uniquely Determined by their Passport

Naiomi Cameron, Mary Kemp, Susan Maslak, Gabrielle Melamed, Richard A. Moy, Jonathan Pham, Austin Wei

Journal-ref: Involve 12 (2019) 791-812

Subjects: Number Theory (math.NT)

[107] arXiv:1805.07750 [pdf, other]

Title: The orbit method and analysis of automorphic forms

Paul D. Nelson, Akshay Venkatesh

Comments: 148 pages. revisions to sections 5.3, 8.8, 17.4, minor edits elsewhere; many clarifications added; to appear in Acta Math

Journal-ref: Acta Math. 226 (2021), no. 1, 1-209

Subjects: Number Theory (math.NT); Analysis of PDEs (math.AP); Representation Theory (math.RT)

[108] arXiv:1805.07751 [pdf, other]

Title: A Database of Belyi Maps

Michael Musty, Sam Schiavone, Jeroen Sijsling, John Voight

Comments: ANTS final revision

Journal-ref: Open Book Series 2 (2019) 375-392

Subjects: Number Theory (math.NT)

[109] arXiv:1805.07787 [pdf, other]

Title: $\lambda$-analogues of r-Stirling numbers of the first kind

Taekyun Kim, Dae san Kim

Comments: 12

Subjects: Number Theory (math.NT)

[110] arXiv:1805.07811 [pdf, other]

Title: Best simultaneous Diophantine approximations for some pairs of algebraic numbers

Gustavo Antonio Pavani

Comments: This is not the final version and it may contain some errors

Subjects: Number Theory (math.NT)

[111] arXiv:1805.07967 [pdf, other]

Title: Set-theoretical entropies of Euler's totient function and other number theoretical special functions

Fatemah Ayatollah Zadeh Shirazi, Reza Yaghmaeian

Comments: 7 pages

Journal-ref: Proceedings of the 16th Annual (International) Conference of the Society for Special Functions and their Applications, 2-4 Nov 2017, Bikaner, India, 87-95

Subjects: Number Theory (math.NT)

[112] arXiv:1805.07990 [pdf, other]

Title: Independence of Artin L-functions

Mircea Cimpoeas, Florin Nicolae

Comments: 10 pages, minor changes, reference added

Subjects: Number Theory (math.NT)

[113] arXiv:1805.08007 [pdf, other]

Title: Purely Periodic and Transcendental Complex Continued Fractions

Gerardo Gonzalez Robert

Comments: Minor typos were fixed and color images are now black and white. The paper will appear in Acta Arithmetica

Subjects: Number Theory (math.NT)

[114] arXiv:1805.08029 [pdf, other]

Title: Cycle integrals of modular functions, Markov geodesics and a conjecture of Kaneko

Paloma Bengoechea, Ozlem Imamoglu

Subjects: Number Theory (math.NT)

[115] arXiv:1805.08056 [pdf, other]

Title: Explicit formulas of Euler sums via multiple zeta values

Ce Xu, Weiping Wang

Subjects: Number Theory (math.NT)

[116] arXiv:1805.08103 [pdf, other]

Title: Induction and restriction of (\phi,\Gamma)-modules

Ehud de Shalit, Gal Porat

Comments: 19 pages

Subjects: Number Theory (math.NT)

[117] arXiv:1805.08383 [pdf, other]

Title: On the rationality of algebraic monodromy groups of compatible systems

Chun Yin Hui

Comments: Accepted in JEMS

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

[118] arXiv:1805.08448 [pdf, other]

Title: On the theory of higher rank Euler, Kolyvagin and Stark systems, II

David Burns, Ryotaro Sakamoto, Takamichi Sano

Comments: 51 pages

Subjects: Number Theory (math.NT)

[119] arXiv:1805.08471 [pdf, other]

Title: Nodal intersections for arithmetic random waves against a surface

Riccardo Walter Maffucci

Comments: 50 pages

Journal-ref: Annales Henri Poincar\'e, 20(11):3651-3691, 2019

Subjects: Number Theory (math.NT)

[120] arXiv:1805.08475 [pdf, other]

Title: Evaluation of Gaussian hypergeometric series using Huff's models of elliptic curves

Mohammad Sadek, Nermine El-Sissi, Arman Shamsi Zargar, Naser Zamani

Journal-ref: The Ramanujan Journal, Volume 48, Number 2 (2019), 357--368

Subjects: Number Theory (math.NT)

[121] arXiv:1805.08579 [pdf, other]

Title: Smallest representatives of $\operatorname{SL}(2,\mathbb Z)$-orbits of binary forms and endomorphisms of ${\mathbb P}^1$

Benjamin Hutz, Michael Stoll

Comments: 23 pages, 1 figure; v2: Extended introduction, some minor changes following referee's recommendations

Journal-ref: Acta Arith. 189, 283-308 (2019)

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

[122] arXiv:1805.08648 [pdf, other]

Title: Some truncated identities of Gauss

Bing He

Comments: Critical comments are always welcome

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

[123] arXiv:1805.08759 [pdf, other]

Title: Asymptotics for the Fourier coefficients of eta-quotients

Shane Chern

Subjects: Number Theory (math.NT)

[124] arXiv:1805.08793 [pdf, other]

Title: Familles de formes modulaires de Drinfeld pour le groupe g\'en\'eral lin\'eaire

Marc-Hubert Nicole, Giovanni Rosso

Comments: In French. 35 pages. To appear in Transactions of the A.M.S

Subjects: Number Theory (math.NT)

[125] arXiv:1805.08811 [pdf, other]

Title: Some multidimensional integrals in number theory and connections with the Painlev\'e V equation

Estelle Basor, Fan Ge, Michael O. Rubinstein

Subjects: Number Theory (math.NT)

[126] arXiv:1805.08851 [pdf, other]

Title: Non-invariance of weak approximation properties under extension of the ground field

Yongqi Liang

Comments: Comments are welcome

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

[127] arXiv:1805.08869 [pdf, other]

Title: On Abhyankar's lemma about ramification indices

Jean-Luc Chabert, Emmanuel Halberstadt

Comments: 3 pages

Subjects: Number Theory (math.NT)

[128] arXiv:1805.08873 [pdf, other]

Title: Rigorous Analysis of a Randomised Number Field Sieve

Jonathan Lee, Ramarathnam Venkatesan

Journal-ref: J. of Number Theory Vol. 187 (2018) 92-159

Subjects: Number Theory (math.NT)

[129] arXiv:1805.08910 [pdf, other]

Title: Sum-product estimates over arbitrary finite fields

Doowon Koh, Sujin Lee, Thang Pham, Chun-Yen Shen

Comments: 16 pages

Subjects: Number Theory (math.NT)

[130] arXiv:1805.08996 [pdf, other]

Title: Reflective automorphic forms on lattices of squarefree level

Moritz Dittmann

Subjects: Number Theory (math.NT)

[131] arXiv:1805.09008 [pdf, other]

Title: On the average number of representations of an integer as a sum of like prime powers

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

Comments: Final version. References updated. To appear in Proc. AMS

Journal-ref: Proc. Amer. Math. Soc. 148.4 (2020), 1499-1508

Subjects: Number Theory (math.NT)

[132] arXiv:1805.09225 [pdf, other]

Title: On the congruences of Eisenstein series with polynomial indexes

Su Hu, Min-Soo Kim, Min Sha

Comments: 17 pages

Subjects: Number Theory (math.NT)

[133] arXiv:1805.09373 [pdf, other]

Title: On the cohomology of congruence subgroups of GL3 over the Eisenstein integers

Paul E. Gunnells, Mark McConnell, Dan Yasaki

Subjects: Number Theory (math.NT)

[134] arXiv:1805.09500 [pdf, other]

Title: On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products

Nils Matthes, Koji Tasaka

Comments: 22 pages, final version, to appear in Kyushu J. Math

Subjects: Number Theory (math.NT)

[135] arXiv:1805.09630 [pdf, other]

Title: Arithmetic analogues of Hamiltonian systems

Alexandru Buium

Subjects: Number Theory (math.NT)

[136] arXiv:1805.09636 [pdf, other]

Title: Invariant Frobenius lifts and deformation of the Hasse invariant

Alexandru Buium

Subjects: Number Theory (math.NT)

[137] arXiv:1805.09671 [pdf, other]

Title: Computing the ideal class monoid of an order

Stefano Marseglia

Comments: final version

Journal-ref: J. Lond. Math. Soc. (2) 101 (2020), no. 3, 984-1007

Subjects: Number Theory (math.NT)

[138] arXiv:1805.09677 [pdf, other]

Title: Proofs for two Lambert series identities of Gosper

Bing He

Comments: Critical comments are always welcome

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

[139] arXiv:1805.09729 [pdf, other]

Title: Gauss sums of some matrix groups over $\Bbb Z/n\Bbb Z$

Su Hu, Guoxing He, Yingtong Meng, Yan Li

Comments: 14 pages

Subjects: Number Theory (math.NT)

[140] arXiv:1805.09761 [pdf, other]

Title: Expansions of the Riemann Zeta function in the critical strip

B.Candelpergher

Comments: 18 pages

Subjects: Number Theory (math.NT)

[141] arXiv:1805.09777 [pdf, other]

Title: Compatible systems of Galois representations associated to the exceptional group E6

George Boxer, Frank Calegari, Matthew Emerton, Brandon Levin, Keerthi Madapusi Pera, Stefan Patrikis

Comments: bibliography fixed in new version. comments welcome

Subjects: Number Theory (math.NT)

[142] arXiv:1805.09794 [pdf, other]

Title: ExactpAdics: An exact representation of p-adic numbers

Christopher Doris

Comments: 55 pages; code available from this https URL and this https URL

Subjects: Number Theory (math.NT)

[143] arXiv:1805.09809 [pdf, other]

Title: On Unfoldings of Some Integrals of Automorphic Functions on General Linear Groups

Eleftherios Tsiokos

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

[144] arXiv:1805.10104 [pdf, other]

Title: Transcendence and linear relations of $1$-periods

Annette Huber, Gisbert Wüstholz

Comments: This is the final draft and very close to the published version of the monograph, but not identical. In particular layout and page numbers do not agree. To appear: Cambridge Tracts in Mathematics 227, Cambridge University Press, May 2022. Copyright Annette Huber and Gisbert Wüstholz

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

[145] arXiv:1805.10151 [pdf, other]

Title: Calculations of the invariant measure for Hurwitz Continued Fractions

Ghaith Hiary, Joseph Vandehey

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

[146] arXiv:1805.10303 [pdf, other]

Title: Improved estimate for the prime counting function $\pi(x)$

Theophilus Agama

Comments: Improvement of the previous version suggested by the referee

Subjects: Number Theory (math.NT)

[147] arXiv:1805.10361 [pdf, other]

Title: On the number of Galois orbits of newforms

Luis Dieulefait, Ariel Pacetti, Panagiotis Tsaknias

Comments: 26 pages

Subjects: Number Theory (math.NT)

[148] arXiv:1805.10436 [pdf, other]

Title: Hausdorff dimension in inhomogeneous Diophantine approximation

Yann Bugeaud, Dong Han Kim, Seonhee Lim, Michał Rams

Comments: 16 pages

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

[149] arXiv:1805.10452 [pdf, other]

Title: Weil sums of binomials: properties, applications, and open problems

Daniel J. Katz

Comments: 26 pages

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

[150] arXiv:1805.10468 [pdf, other]

Title: A short note on the multiplicative energy of the spectrum of a set

Ilya D. Shkredov

Comments: 10 pages

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