arXiv math.NT Number Theory (@mathNTb) / X

arXiv math.NT Number Theory

54.3K posts

arXiv math.NT Number Theory

@mathNTb

Unofficial bot by @vela with github.com/so-okada/twXiv. @mathMPb @mathNAb @mathOAb @mathOCb @mathPRb @mathQAb @mathRAb @mathRTb @mathSGb @mathSPb ...

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Joined April 2013

arXiv math.NT Number Theory
@mathNTb
Dec 6, 2024
Hanamichi Kawamura, Anju Yokoi: Cyclic sum formula for certain parametrized multiple zeta values arxiv.org/abs/2412.04089 arxiv.org/pdf/2412.04089
arxiv.org
Cyclic sum formula for certain parametrized multiple zeta values
Ohno-Wakabayashi's cyclic sum formula for multiple zeta-star values is generalized by Igarashi with one or two parameters. In this article, we give a possible answer for one of his problems about...
562K
arXiv math.NT Number Theory
@mathNTb
Nov 23, 2023
Yuhi Kamio, Junnosuke Koizumi, Toshihiko Nakazawa: Quadratic residues and domino tilings arxiv.org/abs/2311.13597 arxiv.org/pdf/2311.13597
arxiv.org
Quadratic residues and domino tilings
The formula for the number of domino tilings due to Kasteleyn and Temperley-Fisher is strikingly similar to Eisenstein's formula for the Legendre symbol. We study the connection between these two...
170K
arXiv math.NT Number Theory
@mathNTb
Aug 20, 2025
Anju Yokoi: An interpolation of Bradley's sum formula arxiv.org/abs/2508.13254 arxiv.org/pdf/2508.13254 arxiv.org/html/2508.13254
arxiv.org
An interpolation of Bradley's sum formula
The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.
74K
arXiv math.NT Number Theory
@mathNTb
Dec 22, 2023
Hanamichi Kawamura: Formal sine functions in harmonic algebra arxiv.org/abs/2312.13525 arxiv.org/pdf/2312.13525
arxiv.org
Formal sine functions in harmonic algebra
In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula...
194K
arXiv math.NT Number Theory
@mathNTb
Sep 1, 2025
Yuya Murakami: A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture arxiv.org/abs/2508.21710 arxiv.org/pdf/2508.21710 arxiv.org/html/2508.21710
arxiv.org
A framework for proving quantum modularity: Application to...
We address two linked problems at the interface of quantum topology and number theory: deriving asymptotic expansions of the Witten--Reshetikhin--Turaev invariants for 3-manifolds and establishing...
139K
arXiv math.NT Number Theory
@mathNTb
May 13, 2024
William Craig, Jan-Willem van Ittersum, Ken Ono: Integer partitions detect the primes arxiv.org/abs/2405.06451 arxiv.org/pdf/2405.06451
52K
arXiv math.NT Number Theory
@mathNTb
Jan 29, 2025
Terence Tao, Tim Trudgian, Andrew Yang: New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach arxiv.org/abs/2501.16779 arxiv.org/pdf/2501.16779 arxiv.org/html/2501.16779
arxiv.org
New exponent pairs, zero density estimates, and zero additive...
We obtain several new bounds on exponents of interest in analytic number theory, including four new exponent pairs, new zero density estimates for the Riemann zeta-function, and new estimates for...
16K
arXiv math.NT Number Theory
@mathNTb
Aug 15, 2024
Tom Leinster: Galois Theory arxiv.org/abs/2408.07499 arxiv.org/pdf/2408.07499
arxiv.org
Galois Theory
These are the notes for an undergraduate course at the University of Edinburgh, 2021-2023. Assuming basic knowledge of ring theory, group theory and linear algebra, the notes lay out the theory of...
3.7K
arXiv math.NT Number Theory
@mathNTb
Sep 28, 2022
Hanamichi Kawamura: Iterated integrals associated with colored rooted trees arxiv.org/abs/2209.13293 arxiv.org/pdf/2209.13293
arxiv.org
Iterated integrals associated with colored rooted trees
In this paper, we introduce iterated integrals associated with colored rooted trees and give proofs for the shuffle relations for $\boldsymbol{p}$-adic finite and $t$-adic symmetric...
arXiv math.NT Number Theory
@mathNTb
Nov 15, 2022
Martin Brandenburg: A simple proof of the fundamental theorem of Galois theory arxiv.org/abs/2211.07508 arxiv.org/pdf/2211.07508
arXiv math.NT Number Theory
@mathNTb
Dec 6, 2024
Stavros Garoufalidis, Peter Scholze, Campbell Wheeler, Don Zagier: The Habiro ring of a number field arxiv.org/abs/2412.04241 arxiv.org/pdf/2412.04241
arxiv.org
The Habiro ring of a number field
We introduce the Habiro ring of a number field $\mathbb{K}$ and modules over it graded by $K_3(\mathbb{K})$. Elements of these modules are collections of power series at each complex root of unity...
16K
arXiv math.NT Number Theory
@mathNTb
Jan 14, 2025
Connes, Consani: Knots, primes and class field theory arxiv.org/abs/2501.06560 arxiv.org/pdf/2501.06560 arxiv.org/html/2501.06560
arxiv.org
Knots, primes and class field theory
In this paper, we present a geometric generalization of class field theory, demonstrating how adelic constructions, central to the spectral realization of zeros of L-functions and the geometric...
4K
arXiv math.NT Number Theory
@mathNTb
Jan 19, 2024
Masanobu Kaneko, Toshiki Matsusaka, Shin-ichiro Seki: On finite analogues of Euler's constant arxiv.org/abs/2401.09935 arxiv.org/pdf/2401.09935
32K
arXiv math.NT Number Theory
@mathNTb
Mar 5, 2025
Yuhi Kamio: Asymptotic Analysis of Infinite Decompositions of a Unit Fract... arxiv.org/abs/2503.02317 arxiv.org/pdf/2503.02317 arxiv.org/html/2503.02317
arxiv.org
Asymptotic Analysis of Infinite Decompositions of a Unit Fraction...
Paul Erdős posed a problem on the asymptotic estimation of decomposing 1 into a sum of infinitely many unit fractions in \cite{Erd80}. We point out that this problem can be solved in the same...
5.6K