Sun's Series via Cyclotomic Multiple Zeta Values

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-12 DOI:10.3842/sigma.2023.074

Yajun Zhou

引用次数: 1

Abstract

We prove and generalize several recent conjectures of Z.-W. Sun surrounding binomial coefficients and harmonic numbers. We show that Sun's series and their analogs can be represented as cyclotomic multiple zeta values of levels $N\in\{4,8,12,16,24\}$, namely Goncharov's multiple polylogarithms evaluated at $N$-th roots of unity.

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太阳的系列通过环切多重Zeta值

我们证明并推广了最近关于z - w的几个猜想。太阳周围二项式系数和调和数。我们证明Sun的级数和它们的类似物可以表示为在\{4,8,12,16,24\}$中$N阶的多个zeta值，即在$N$-单位根处求值的Goncharov的多重多对数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.