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Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula

Published online by Cambridge University Press:  20 November 2018

Driss Essouabri ,
Kohji Matsumoto  and
Hirofumi Tsumura
Driss Essouabri
Affiliation:
PRES Université de Lyon, Université Jean-Monnet (Saint-Etienne), Faculté des Sciences, Département de Mathématiques, 42023 Saint-Etienne Cedex 2, France email: driss.essouabri@univ-st-etienne.fr
Kohji Matsumoto
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan email: kohjimat@math.nagoya-u.ac.jp
Hirofumi Tsumura
Affiliation:
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397 Japan email: tsumura@tmu.ac.jp
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Abstract

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We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, we introduce more general vectorial zeta-functions and prove their holomorphic continuation. Moreover, we show a vectorial sum formula among those vectorial zeta-functions from which some generalizations of the classical sum formula can be deduced.

Keywords

11M4140B0511B39Zeta-functionsholomorphic continuationrecurrence sequencesFibonacci numberssum formulas
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 2 , 01 April 2011 , pp. 241 - 276
Copyright
Copyright © Canadian Mathematical Society 2012

References

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