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Analytic continuation of multiple zeta functions

Authors:	Jianqiang Zhao

Affiliation:	Department of Mathematics, Brown University, Providence, Rhode Island 02912

Abstract:	In this paper we shall define the analytic continuation of the multiple (Euler-Riemann-Zagier) zeta functions of depth : $begin{displaymath}zeta(s_1,dots,s_d):= sum _{0<n_1 < n_2<cdots<n_d} frac{1}{n_1^{s_1}n_2^{s_2}cdots n_d^{s_d}},end{displaymath}$ where and $sum _{j=1}^dre(s_j)>d$ . We shall also study their behavior near the poles and pose some open problems concerning their zeros and functional equations at the end.

Keywords:	Analytic continuation multiple zeta function generalized function

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