On the Set of Points Represented by Harmonic Subseries.

Authors: Kovač, Vjekoslav (AUTHOR) vjekovac@math.hr

Source: American Mathematical Monthly. Nov2025, Vol. 132 Issue 9, p895-911. 17p.

Subject Terms: *ARITHMETIC combinatorics, *TOPOLOGICAL spaces, *MATHEMATICIANS, *IDENTITIES (Mathematics), *NATURAL numbers, *SUBHARMONIC functions

Normal covering numbers for Sn and An and additive combinatorics.

Authors: Eberhard, Sean¹ (AUTHOR) sean.eberhard@warwick.ac.uk, Mellon, Connor² (AUTHOR)

Source: Bulletin of the London Mathematical Society. Nov2025, Vol. 57 Issue 11, p3307-3325. 19p.

Subject Terms: *NONABELIAN groups, *ARITHMETIC combinatorics, *GROUP theory

Mean value theorems in multiplicative systems and joint ergodicity of additive and multiplicative actions

Authors: Charamaras, Dimitrios

Source: Transactions of the American Mathematical Society. 378:1883-1937

Subject Terms: Relations between ergodic theory and number theory, Arithmetic combinatorics, higher degree uniformity, multiplicative structures of the integers, Ergodic theorems, spectral theory, Markov operators, multiplicative systems, Mathematics - Number Theory, Primary: 37A44, Secondary: 11N37, 11B30, additive ergodic average, FOS: Mathematics, Asymptotic results on arithmetic functions, Dynamical Systems (math.DS), Number Theory (math.NT), Mathematics - Dynamical Systems

File Description: application/xml

Access URL: http://arxiv.org/abs/2403.13744
https://zbmath.org/8004993
https://doi.org/10.1090/tran/9321

Separating measurable recurrence from strong recurrence via rigidity sequences

Authors: Griesmer, John T.

Source: Discrete and Continuous Dynamical Systems. 45:3411-3432

Subject Terms: thin sets, 0102 computer and information sciences, Dynamical Systems (math.DS), 01 natural sciences, 11B30, 37A45, Arithmetic combinatorics, higher degree uniformity, Kronecker sets, Poincaré recurrence, weak mixing, FOS: Mathematics, Relations of ergodic theory with number theory and harmonic analysis, Mathematics - Dynamical Systems, 0101 mathematics, rigidity sequence

File Description: application/xml

Access URL: http://arxiv.org/abs/1808.05609
https://zbmath.org/8037076
https://doi.org/10.3934/dcds.2025024

The Furstenberg–Sárközy theorem for polynomials in one or more prime variables

Authors: Doyle, John R., Rice, Alex^{Aff2, IDs11139025011208_cor1}

Source: The Ramanujan Journal: An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan. 67(3)

Extensions of the triangular D(3)-Pair {3, 6}.

Authors: Filipin, Alan, Jurasić, Ana, Szalay, László

Source: Mathematica Slovaca; Aug2025, Vol. 75 Issue 4, p775-790, 16p

Subject Terms: NUMBER theory, MATHEMATICAL proofs, POLYGONAL numbers, INTEGERS, ARITHMETIC combinatorics

Quantitative expansivity for ergodic Zd$\mathbb {Z}^d$‐actions: Quantitative expansivity for ergodic \(\mathbb{Z}^d\)-actions

Authors: Fish, Alexander, Skinner, Sean

Source: Journal of the London Mathematical Society. 111

Subject Terms: Arithmetic combinatorics, higher degree uniformity, Ramsey theory, FOS: Mathematics, Notions of recurrence and recurrent behavior in topological dynamical systems, Dynamical Systems (math.DS), Mathematics - Dynamical Systems

File Description: application/xml

Access URL: http://arxiv.org/abs/2409.18363
https://zbmath.org/8037467
https://doi.org/10.1112/jlms.70154

A density version of Hua’s theorem

Authors: Tan, Maoru^{j_forum-2024-0521_aff_001}

Source: Forum Mathematicum.

Availability: https://www.degruyter.com/document/doi/10.1515/forum-2024-0521/html

Semigroups of ideals and isomorphism problems

Authors: García-Sánchez, Pedro A., Tringali, Salvatore

Source: Proceedings of the American Mathematical Society.

Subject Terms: Arithmetic combinatorics, higher degree uniformity, Ideal theory for semigroups, Archimedean-like properties, Semigroups in automata theory, linguistics, etc, semigroup ideals, Rings and Algebras (math.RA), power semigroups, isomorphism problems, FOS: Mathematics, Mathematics - Combinatorics, Mathematics - Rings and Algebras, Combinatorics (math.CO), Arithmetic theory of semigroups

File Description: application/xml

Access URL: http://arxiv.org/abs/2410.15622
https://zbmath.org/8027628
https://doi.org/10.1090/proc/17122

On generalized Narkiewicz constants of finite abelian groups

Authors: Gao, Weidong, Hui, Wanzhen, Li, Xue, Li, Yuanlin, Qu, Yongke, Zhong, Qinghai

Source: Acta Arithmetica. 212:133-172

Subject Terms: Arithmetic combinatorics, higher degree uniformity, Finite abelian groups, combinatorial constants for abelian groups, zero-sum sequences, Inverse problems of additive number theory, including sumsets, non-unique factorization, Units and factorization

File Description: application/xml

On the distribution of quadratic residues

Authors: Shkredov, I.D. ^{a, b, ⁎}

Source: In Finite Fields and Their Applications March 2025 103

Additive combinatorics and Diophantine problems

Authors: Chapman, Jonathan

Contributors: Robertson, Donald

Subject Terms: Higher order Fourier Analysis, Arithmetic combinatorics, Arithmetic Ramsey theory, Number theory, Partition regularity, Combinatorics

Access URL: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.843511

Additive and multiplicative Sidon sets.

Authors: Roche-newton, O.¹ (AUTHOR), Warren, A.¹ (AUTHOR) audie.warren@oeaw.ac.at

Source: Acta Mathematica Hungarica. Dec2021, Vol. 165 Issue 2, p326-336. 11p.

Subject Terms: *LOGICAL prediction, *ARITHMETIC combinatorics

Towards characterizing the 2-Ramsey equations of the form ax + by = p(z)

Authors: Baja, Zsolt ^a, Dobák, Dániel ^b, Kovács, Benedek ^c, Pach, Péter Pál ^{d, e, f, ⁎}, Pigler, Donát ^g

Source: In Discrete Mathematics May 2023 346(5)

Simplices in large sets and directional expansion in ergodic actions

Authors: Michael Björklund, Alexander Fish

Source: Forum of Mathematics, Sigma, Vol 12 (2024)

Subject Terms: Relations between ergodic theory and number theory, 11B30, Ergodic theorems, spectral theory, Markov operators, 37A44, Dynamical systems involving one-parameter continuous families of measure-preserving transformations, 37A30, Arithmetic combinatorics, higher degree uniformity, cyclic subgroups, QA1-939, Mathematics - Combinatorics, ergodic \(\mathbb{Z}^r\)-actions, infinite arithmetic progression, Mathematics - Dynamical Systems, Mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.03724
https://doaj.org/article/93e1c9bc78004d6caabbc61d6ef0019b

Arithmetic combinatorics on Vinogradov systems.

Authors: Mudgal, Akshat¹ (AUTHOR)

Source: Transactions of the American Mathematical Society. Aug2020, Vol. 373 Issue 8, p5491-5516. 26p.

Subject Terms: *MEAN value theorems, *ARITHMETIC combinatorics

A convex set with a rich difference

Authors: Roche-Newton, O.^{Aff1, IDs10474022012863_cor1}, Warren, A.

Source: Acta Mathematica Hungarica. 168(2):587-592

On some applications of GCD sums to arithmetic combinatorics

Authors: Shkredov, Ilya D. ¹

Source: In Journal of Number Theory February 2022 231:433-450

SIDON SETS IN A UNION OF INTERVALS

Authors: RIBLET, R.^{Aff1, IDs1047402201246x_cor1}

Source: Acta Mathematica Hungarica. 167(2):533-547

Binary Quadratic Forms in Difference Sets

Authors: Rice, Alex^Aff2

Contributors: Nathanson, Melvyn B., editor^Aff1

Source: Combinatorial and Additive Number Theory III : CANT, New York, USA, 2017 and 2018. 297:175-196