The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions I

被引：57

作者：

Matsumoto, K ^{[1
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

JOURNAL OF NUMBER THEORY | 2003年 / 101卷 / 02期

关键词：

multiple zeta-function; Mellin-Barnes formula; analytic continuation; asymptotic expansion;

D O I：

10.1016/S0022-314X(03)00041-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider general multiple zeta-functions of multi-variables, including both Barnes multiple zeta-functions and Euler-Zagier sums as special cases. We prove the meromorphic continuation to the whole space, asymptotic expansions, and upper bound estimates. These results are expected to have applications to some arithmetical L-functions (such as of Hecke and of Shintani). The method is based on the classical Mellin-Barnes integral formula. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：223 / 243

页数：21

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