Values at non-positive integers of generalized Euler-Zagier multiple zeta-functions

2017/03/22 by Driss Essouabri, Essouabri, Driss, Kohji Matsumoto +1 · 2 citations
Mathematics · #11M32 #11M41 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.07525

openalex publication_date 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give new closed and explicit formulas for "multiple zeta values" at non-positive integers of generalized Euler-Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions and then use the analyticity of the values on the parameters defining the multiple zeta-functions to deduce the formulas in the general case. Also, for our aim we prove an extension of "Raabe's lemma" due to E. Friedman and A. Pereira.

Cited by

• Stirling polynomials and multiple zeta (star) functions at non-positive integers
• Values at non-positive integers of partially twisted multiple zeta-functions II

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