Asymptotic Expansions of Multiple Zeta Functions and Power Mean Values of Hurwitz Zeta Functions

2002 ◽  
Vol 66 (1) ◽  
pp. 41-60 ◽  
Author(s):  
Shigeki Egami ◽  
Kohji Matsumoto
Keyword(s):  
Asymptotic Expansions ◽  
Zeta Functions ◽  
Power Mean ◽  
Mean Values ◽  
Multiple Zeta

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

2003 ◽  
Vol 172 ◽  
pp. 59-102 ◽  
Author(s):  
Kohji Matsumoto
Keyword(s):  
Analytic Continuation ◽  
Eisenstein Series ◽  
Asymptotic Expansions ◽  
Zeta Functions ◽  
Basic Technique ◽  
The Third ◽  
Multiple Zeta ◽  
Double Zeta

AbstractThe 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.

scholarly journals On the Mean Values of Certain Character Sums

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Zhefeng Xu ◽  
Huaning Liu
Keyword(s):  
Character Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Mean Values ◽  
Asymptotic Formulae ◽  
Fourth Power Mean ◽  
The Mean

Letq≥5be an odd number. In this paper, we study the fourth power mean of certain character sums∑χmodq,χ-1=-1*∑1≤a≤q/4aχa4and∑χmodq,χ-1=1*∑1≤a≤q/4aχa4, where∑‍*denotes the summation over primitive characters moduloq, and give some asymptotic formulae.

Periods, Multiple Zeta Functions and ζ(3)

2014 ◽  
pp. 185-203
Author(s):  
M. Ram Murty ◽  
Purusottam Rath
Keyword(s):  
Zeta Functions ◽  
Multiple Zeta

scholarly journals Desingularization of complex multiple zeta-functions

2017 ◽  
Vol 139 (1) ◽  
pp. 147-173 ◽  
Author(s):  
Hidekazu Furusho ◽  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Zeta Functions ◽  
Multiple Zeta
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