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Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series

Published online by Cambridge University Press:  22 January 2016

Kohji Matsumoto
Kohji Matsumoto*
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japankohjimat@math.nagoya-u.ac.jp
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Abstract

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The present paper contains three main results. The first is asymptotic expansions of Barnes double zeta-functions, and as a corollary, asymptotic expansions of holomorphic Eisenstein series follow. The second is asymptotic expansions of Shintani double zeta-functions, and the third is the analytic continuation of n-variable multiple zeta-functions (or generalized Euler-Zagier sums). The basic technique of proving those results is the method of using the Mellin-Barnes type of integrals.

Keywords

11M41
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 172 , 2003 , pp. 59 - 102
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

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