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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
PRES Université de Lyon, Université Jean-Monnet (Saint-Etienne), Faculté des Sciences, Département de Mathématiques, 42023 Saint-Etienne Cedex 2, France email:
Kohji Matsumoto
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan email:
Hirofumi Tsumura
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397 Japan email:
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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.

Research Article
Copyright © Canadian Mathematical Society 2012


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