Number Theory

Authors and titles for May 2018

[151] arXiv:1805.10496 [pdf, other]

Title: A Dual-Radix Approach to Steiner's 1-Cycle Theorem

Andrey Rukhin

Comments: Minor edits; 16 pages; to appear in the proceedings of the "Combinatorial and Additive Number Theory (CANT) 2018" conference

Subjects: Number Theory (math.NT)

[152] arXiv:1805.10501 [pdf, other]

Title: The Riemann-Roch strategy, Complex lift of the Scaling Site

Alain Connes, Caterina Consani

Comments: 67 pages, 6 figures

Subjects: Number Theory (math.NT); Quantum Algebra (math.QA)

[153] arXiv:1805.10569 [pdf, other]

Title: Settling some sum suppositions

Tanay Wakhare, Christophe Vignat

Comments: 13 pages

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

[154] arXiv:1805.10709 [pdf, other]

Title: Ranks, $2$-Selmer groups, and Tamagawa numbers of elliptic curves with $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/8\mathbb{Z}$-torsion

Stephanie Chan, Jeroen Hanselman, Wanlin Li

Journal-ref: Open Book Series 2 (2019) 173-189

Subjects: Number Theory (math.NT)

[155] arXiv:1805.10715 [pdf, other]

Title: Density of rational points on a quadric bundle in $\mathbb{P}^3\times \mathbb{P}^3$

T.D. Browning, D.R. Heath-Brown

Comments: 60 pages; minor edits and added a reference to recent work of Lehmann and Tanimoto, where it is confirmed that the thin set we remove is the one predicted by the Lehmann-Sengupta-Tanimoto machinery

Journal-ref: Duke Math. J. 169, no. 16 (2020), 3099-3165

Subjects: Number Theory (math.NT)

[156] arXiv:1805.10739 [pdf, other]

Title: About Some Relatives of the Taxicab Number

Viorel Nitica

Comments: This version has some minor corrections

Journal-ref: J. of Int. Seq., 21 (2018), Article 18.9.4

Subjects: Number Theory (math.NT)

[157] arXiv:1805.10873 [pdf, other]

Title: On the paramodularity of typical abelian surfaces (and reduction of G-covariant bilinear forms)

Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, John Voight, David S. Yuen (appendix by J.P. Serre)

Comments: 49 pages; proof of Lemma 4.3.6 simplified, still with the new appendix by Serre

Journal-ref: Alg. Number Th. 13 (2019) 1145-1195

Subjects: Number Theory (math.NT)

[158] arXiv:1805.10877 [pdf, other]

Title: On certain sums concerning the gcd's and lcm's of $k$ positive integers

Titus Hilberdink, Florian Luca, László Tóth

Comments: 14 pages, revised

Journal-ref: International Journal of Number Theory, Vol. 16, No. 1 (2020) 77-90

Subjects: Number Theory (math.NT)

[159] arXiv:1805.10897 [pdf, other]

Title: Stochastic Canonical Heights

Vivian Olsiewski Healey, Wade Hindes

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

[160] arXiv:1805.10937 [pdf, other]

Title: Raising the level at your favorite prime

Luis Dieulefait, Eduardo Soto

Comments: 13 pages

Subjects: Number Theory (math.NT)

[161] arXiv:1805.11066 [pdf, other]

Title: The density function for the value-distribution of the Lerch zeta-function and its applications

Masahiro Mine

Comments: 37 pages

Journal-ref: Michigan Math. J. 69 (2020) 849-889

Subjects: Number Theory (math.NT)

[162] arXiv:1805.11071 [pdf, other]

Title: On the semi-simplicity conjecture for $\mathbb{Q}^{ab}$

Marco D'Addezio

Comments: 7 pages; §3 expanded

Journal-ref: Math. Res. Lett. 29 (2022), 1003-1009

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

[163] arXiv:1805.11072 [pdf, other]

Title: On certain mean values of logarithmic derivatives of $L$-functions and the related density functions

Masahiro Mine

Comments: 19 pages

Journal-ref: Funct. Approx. Comment. Math. 61 (2019) 179-199

Subjects: Number Theory (math.NT)

[164] arXiv:1805.11152 [pdf, other]

Title: A finiteness theorem for specializations of dynatomic polynomials

David Krumm

Journal-ref: Alg. Number Th. 13 (2019) 963-993

Subjects: Number Theory (math.NT)

[165] arXiv:1805.11153 [pdf, other]

Title: Sieve Methods in Random Graph Theory

Yu-Ru Liu, J.C. Saunders

Subjects: Number Theory (math.NT)

[166] arXiv:1805.11205 [pdf, other]

Title: Bounded ranks and Diophantine error terms

Hector Pasten

Subjects: Number Theory (math.NT)

[167] arXiv:1805.11319 [pdf, other]

Title: Asymptotic Formulas Related to the $M_2$-rank of Partitions without Repeated Odd Parts

Chris Jennings-Shaffer, Dillon Reihill

Subjects: Number Theory (math.NT)

[168] arXiv:1805.11502 [pdf, other]

Title: Moments of Spinor L-Functions and symplectic Kloosterman sums

Fabian Waibel

Subjects: Number Theory (math.NT)

[169] arXiv:1805.11585 [pdf, other]

Title: From Polya fields to Polya groups: (I) Galoisian extensions

Jean-Luc Chabert

Comments: 13 pages, 2 figures

Subjects: Number Theory (math.NT)

[170] arXiv:1805.11657 [pdf, other]

Title: On the distribution of primes in the alternating sums of concecutive primes

Romeo Meštrović

Comments: 9 pages, one table, no figures

Subjects: Number Theory (math.NT)

[171] arXiv:1805.11658 [pdf, other]

Title: Fractional jumps: complete characterisation and an explicit infinite family

Federico Amadio Guidi, Giacomo Micheli

Subjects: Number Theory (math.NT)

[172] arXiv:1805.11879 [pdf, other]

Title: Minoration de la hauteur de Weil dans un compositum de corps de rayon

Arnaud Plessis

Comments: 26 pages, in French. Many typos mistakes deleted, the section 5 of the V1 has been deleted

Subjects: Number Theory (math.NT)

[173] arXiv:1805.11880 [pdf, other]

Title: Comparison of probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions

Victor Volfson

Comments: 9 pages

Subjects: Number Theory (math.NT)

[174] arXiv:1805.11922 [pdf, other]

Title: On the operations of sequences in rings and binomial type sequences

Stefano Barbero, Umberto Cerruti, Nadir Murru

Journal-ref: Ricerche di Matematica, 2018

Subjects: Number Theory (math.NT)

[175] arXiv:1805.11991 [pdf, other]

Title: Hyperelliptic Curves over Small Finite Fields and GPU Accelerators

Martin Raum

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

[176] arXiv:1805.12335 [pdf, other]

Title: Drinfeld modular forms of arbitrary rank, Part I: Analytic Theory

Dirk Basson, Florian Breuer, Richard Pink

Comments: 24 pages

Subjects: Number Theory (math.NT)

[177] arXiv:1805.12337 [pdf, other]

Title: Drinfeld modular forms of arbitrary rank, Part II: Comparison with Algebraic Theory

Dirk Basson, Florian Breuer, Richard Pink

Comments: 29 pages

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

[178] arXiv:1805.12339 [pdf, other]

Title: Drinfeld modular forms of arbitrary rank, Part III: Examples

Dirk Basson, Florian Breuer, Richard Pink

Comments: 30 pages

Subjects: Number Theory (math.NT)

[179] arXiv:1805.12464 [pdf, other]

Title: Quasi-shuffle algebras and applications

Michael E. Hoffman

Comments: 25 pages; submission to CARMA proceedings

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

[180] arXiv:1805.12537 [pdf, other]

Title: Groups of automorphisms of p-adic integers and the problem of the existence of fully homomorphic ciphers

Ekaterina Yurova Axelsson, Andrei Khrennikov

Comments: arXiv admin note: text overlap with arXiv:1603.07699

Subjects: Number Theory (math.NT); Cryptography and Security (cs.CR); Data Structures and Algorithms (cs.DS)

[181] arXiv:1805.12538 [pdf, other]

Title: Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces

Francesca Balestrieri, Rachel Newton

Comments: 16 pages. Corrected grant reference number and added journal reference and DOI. arXiv admin note: substantial text overlap with arXiv:1804.05819

Journal-ref: International Mathematics Research Notices, Volume 2021, Issue 6, March 2021, Pages 4255-4279

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

[182] arXiv:1805.12588 [pdf, other]

Title: Tame Galois module structure revisited

Fabio Ferri, Cornelius Greither

Comments: 16 pages. Same version as the published paper

Journal-ref: Ann. Mat. Pura Appl. (2019), https://doi.org/10.1007/s10231-019-00852-x

Subjects: Number Theory (math.NT)

[183] arXiv:1805.00133 (cross-list from math.DS) [pdf, other]

Title: Parity sequences of the 3x+1 map on the 2-adic integers and Euclidean embedding

Olivier Rozier

Comments: 30 pages, 2 figures. Various improvements

Journal-ref: Integers 19 (2019), article A8

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

[184] arXiv:1805.00567 (cross-list from math.AG) [pdf, other]

Title: Hall algebras and graphs of Hecke operators for elliptic curves

Roberto Alvarenga

Comments: 38 pages, comments are welcome - minor typos were corrected in the second version

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

[185] arXiv:1805.02428 (cross-list from math-ph) [pdf, other]

Title: Level repulsion for arithmetic toral point scatterers in dimension $3$

Pär Kurlberg

Comments: 16 pages, 2 figures

Subjects: Mathematical Physics (math-ph); Number Theory (math.NT); Spectral Theory (math.SP); Chaotic Dynamics (nlin.CD)

[186] arXiv:1805.02573 (cross-list from math.RA) [pdf, other]

Title: Studying the Diophantine problem in finitely generated rings and algebras via bilinear maps

Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov

Comments: v2: We improved the organization of the paper and added references

Subjects: Rings and Algebras (math.RA); Logic (math.LO); Number Theory (math.NT)

[187] arXiv:1805.04085 (cross-list from math.GR) [pdf, other]

Title: Diophantine problems in solvable groups

Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov

Comments: New results were added (in particular, several results regarding groups of matrices). Some results were strengthened. Helpful referee suggestions were implemented. 28 pages

Subjects: Group Theory (math.GR); Logic (math.LO); Number Theory (math.NT)

[188] arXiv:1805.04292 (cross-list from math.CO) [pdf, other]

Title: A family of four-variable expanders with quadratic growth

Mehdi Makhul

Comments: 5 pages

Journal-ref: Moscow J. Comb. Number Th. 8 (2019) 143-149

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

[189] arXiv:1805.05490 (cross-list from math.GT) [pdf, other]

Title: Mahler Measure and the Vol-Det Conjecture

Abhijit Champanerkar, Ilya Kofman, Matilde Lalín

Comments: 29 pages. V2: Minor changes, fixed typos, improved exposition

Journal-ref: J. London Math. Soc. (2) 99 (2019), 872-900

Subjects: Geometric Topology (math.GT); Number Theory (math.NT)

[190] arXiv:1805.05496 (cross-list from math.AG) [pdf, other]

Title: Some results about zero-cycles on abelian and semi-abelian varieties

Evangelia Gazaki

Comments: 13 pages

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

[191] arXiv:1805.05549 (cross-list from math.CO) [pdf, other]

Title: Improved Bounds for Progression-Free Sets in $C_{8}^{n}$

Fedor Petrov, Cosmin Pohoata

Comments: 14 pages

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

[192] arXiv:1805.05632 (cross-list from math.DS) [pdf, other]

Title: Some problems of arithmetic origin in rational dynamics

Romain Dujardin (LPSM UMR 8001)

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

[193] arXiv:1805.05678 (cross-list from math.AG) [pdf, other]

Title: Noether's problem for some subgroups of $S_{14}$: the modular case

Hang Fu, Ming-chang Kang, Baoshan Wang, Jian Zhou

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

[194] arXiv:1805.05893 (cross-list from math.CO) [pdf, other]

Title: A $q$-summation and the orthogonality relations for the $q$-Hahn polynomials and the big $q$-Jacobi polynomials

Zhi-Guo Liu

Comments: 22 pages

Journal-ref: Journal of Mathematical Analysis and Applications 419 (2014)1045--1064

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

[195] arXiv:1805.05933 (cross-list from math.CO) [pdf, other]

Title: On supra-SIM sets of natural numbers

Isaac Goldbring, Steven Leth

Comments: 9 pages; preliminary draft; Comments welcome!

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

[196] arXiv:1805.06108 (cross-list from math.CO) [pdf, other]

Title: A generalized Hardy-Ramanujan formula for the number of restricted integer partitions

Tiefeng Jiang, Ke Wang

Comments: 27 pages. Final version. Accepted by Journal of Number Theory

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

[197] arXiv:1805.06560 (cross-list from math.CO) [pdf, other]

Title: Extensions of Ramanujan's reciprocity theorem and the Andrews--Askey integral

Zhi-Guo Liu

Comments: 24 pages

Journal-ref: Journal of mathematical analysis and applications (419) 2014, Pages 1045--1064

Subjects: Combinatorics (math.CO); Classical Analysis and ODEs (math.CA); Number Theory (math.NT); Quantum Algebra (math.QA)

[198] arXiv:1805.06575 (cross-list from math.CO) [pdf, other]

Title: Some inequalities for Garvan's bicrank function of 2-colored partitions

Shane Chern, Dazhao Tang, Liuquan Wang

Comments: 27 pages

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

[199] arXiv:1805.07081 (cross-list from math.AG) [pdf, other]

Title: The Test Function Conjecture for Local Models of Weil-restricted groups

Thomas J. Haines, Timo Richarz

Comments: Minor corrections; added §§7-8 on the test function conjecture for modified local models

Journal-ref: Compositio Math. 156 (2020) 1348-1404

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

[200] arXiv:1805.07121 (cross-list from math.AG) [pdf, other]

Title: Motivic periods and Grothendieck arithmetic invariants

F. Andreatta, L. Barbieri-Viale, A. Bertapelle

Comments: Appendix by B. Kahn added. Revised version to appear on Adv. Math

Journal-ref: Advances in Mathematics Vol. 359 (2020) 106880

Subjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT); Number Theory (math.NT)