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Multiple zeta functions: the double sine function and the signed double Poisson summation formula

Published online by Cambridge University Press:  04 December 2007

Shin-ya Koyama  and
Nobushige Kurokawa
Shin-ya Koyama
Affiliation:
Department of Mathematics, Keio University, 223-8522, Japankoyama@math.keio.ac.jp
Nobushige Kurokawa
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 152-8551, Japankurokawa@math.titech.ac.jp
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Abstract

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We construct multiple zeta functions as absolute tensor products of usual zeta functions. The Euler product expression is established for the most basic case $\zeta(s,\mathbf{F}_p)\otimes\zeta(s,\mathbf{F}_q)$ by using the signed double Poisson summation formula and the theory of the double sine function.

Keywords

zeta functionmultiple zeta functionmultiple sine function11M06
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 5 , September 2004 , pp. 1176 - 1190
Copyright
Foundation Compositio Mathematica 2004