Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
- 1 January 2003
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 172, 59-102
- https://doi.org/10.1017/s0027763000008643
Abstract
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
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