Geodesic
Values at non-positive integers of generalized Euler–Zagier multiple zeta-functions
Driss Essouabri 1   ; Kohji Matsumoto 2
1 Univ. 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
2 Graduate School of Mathematics Nagoya University Furo-cho, Chikusa-ku Nagoya 464-8602, Japan
Acta Arithmetica, Tome 193 (2020) no. 2, pp. 109-131 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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).
DOI : 10.4064/aa171120-13-3
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

Driss Essouabri  1   ; Kohji Matsumoto  2

1 Univ. 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
2 Graduate School of Mathematics Nagoya University Furo-cho, Chikusa-ku Nagoya 464-8602, Japan 
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     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},
     year = {2020},
     volume = {193},
     number = {2},
     doi = {10.4064/aa171120-13-3},
     language = {en},
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}
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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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