Values at non-positive integers of generalized Euler–Zagier multiple zeta-functions
Acta Arithmetica, Tome 193 (2020) no. 2, pp. 109-131
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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).
Keywords:
closed explicit formulas multiple zeta values non positive integers generalized euler zagier multiple zeta functions first prove these formulas small convenient class these multiple zeta functions analyticity values parameters defining multiple zeta functions deduce formulas general prove extension raabe lemma due friedman nbsp pereira
Affiliations des auteurs :
Driss Essouabri 1 ; Kohji Matsumoto 2
@article{10_4064_aa171120_13_3,
author = {Driss Essouabri and Kohji Matsumoto},
title = {Values at non-positive integers of generalized {Euler{\textendash}Zagier} multiple zeta-functions},
journal = {Acta Arithmetica},
pages = {109--131},
publisher = {mathdoc},
volume = {193},
number = {2},
year = {2020},
doi = {10.4064/aa171120-13-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa171120-13-3/}
}
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Driss Essouabri; Kohji Matsumoto. Values at non-positive integers of generalized Euler–Zagier multiple zeta-functions. Acta Arithmetica, Tome 193 (2020) no. 2, pp. 109-131. doi: 10.4064/aa171120-13-3
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