Nagoya Mathematical Journal

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

Kohji Matsumoto

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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.

Article information

Source
Nagoya Math. J., Volume 172 (2003), 59-102.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631956

Mathematical Reviews number (MathSciNet)
MR2019520

Zentralblatt MATH identifier
1060.11053

Subjects
Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}

Citation

Matsumoto, Kohji. Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series. Nagoya Math. J. 172 (2003), 59--102. https://projecteuclid.org/euclid.nmj/1114631956


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