Sum formulas of mltiple zeta values with arguments are multiple of a positive integer

2016/08/04 by Kwang-Wu Chen, Chen, Kwang-Wu, Chan-Liang Chung +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1608.01412

16 pages

arxiv created 2016/08/04 · openalex publication_date 2016/08/04 · arxiv updated 2016/08/05 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

For k≤ n, let E(mn,k) be the sum of all multiple zeta values of depth k and weight mn with arguments are multiples of m≥ 2. More precisely, E(mn,k)=∑_{|\boldsymbolα|=n}ζ(mα₁,mα₂,…, mα_k). In this paper, we develop a formula to express E(mn,k) in terms of ζ(\m\^p) and ζ^⋆(\m\^q), 0≤ p,q≤ n. In particular, we settle Genčev's conjecture on the evaluation of E(4n,k) and also evaluate E(mn,k) explicitly for small even m≤ 8.

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