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

Volume 193 / 2020

Driss Essouabri, Kohji Matsumoto Acta Arithmetica 193 (2020), 109-131 MSC: Primary 11M32; Secondary 11M41. DOI: 10.4064/aa171120-13-3 Published online: 17 January 2020


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, we prove an extension of “Raabe’s lemma” due to E. Friedman and A. Pereira (2007).


  • Driss EssouabriUniv. Lyon
    UJM-Saint-Étienne, CNRS
    Institut Camille Jordan UMR 5208
    Faculté des Sciences et Techniques
    23 rue du Docteur Paul Michelon
    F-42023 Saint-Étienne, France
  • Kohji MatsumotoGraduate School of Mathematics
    Nagoya University
    Furo-cho, Chikusa-ku
    Nagoya 464-8602, Japan

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