scholarly journals Part I. Analytic continuation of some zeta functions

2010 ◽  
pp. 1-16
Author(s):  
Gautami Bhowmik
Keyword(s):  
Analytic Continuation ◽  
Zeta Functions

scholarly journals Analytic continuation of multiple zeta-functions and their values at non-positive integers

2001 ◽  
Vol 98 (2) ◽  
pp. 107-116 ◽  
Author(s):  
Shigeki Akiyama ◽  
Shigeki Egami ◽  
Yoshio Tanigawa
Keyword(s):  
Analytic Continuation ◽  
Zeta Functions ◽  
Multiple Zeta ◽  
Positive Integers

A Generalization of Epstein Zeta Functions

1949 ◽  
Vol 1 (4) ◽  
pp. 320-327 ◽  
Author(s):  
S. Minakshisundaram
Keyword(s):  
Zeta Function ◽  
Analytic Continuation ◽  
General Class ◽  
Zeta Functions ◽  
Epstein Zeta Function ◽  
Image Position

§ 1. An Epstein zeta function (in its simplest form) is a function represented by the Dirichlet's series where a1… ak are real and n1, n2, … nk run through integral values. The properties of this function are well known and the simplest of them were proved by Epstein [2, 3]. The aim of this note is to define a general class of Dirichlet's series, of which the above can be viewed as an instance, and to discuss the problem of analytic continuation of such series.

Analytic continuation of multiple Hurwitz zeta functions

2008 ◽  
Vol 145 (3) ◽  
pp. 605-617 ◽  
Author(s):  
JAMES P. KELLIHER ◽  
RIAD MASRI
Keyword(s):  
Zeta Function ◽  
Analytic Continuation ◽  
Zeta Functions ◽  
Hurwitz Zeta Function ◽  
Image Position

AbstractWe use a variant of a method of Goncharov, Kontsevich and Zhao [5, 16] to meromorphically continue the multiple Hurwitz zeta function to $\mathbb{C}^{d}$, to locate the hyperplanes containing its possible poles and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of $\zeta_{d}(s;\theta)$.

scholarly journals Analytic continuation of multiple Hurwitz zeta functions

2017 ◽  
Vol 69 (4) ◽  
pp. 1431-1442
Author(s):  
Jay MEHTA ◽  
G. K. VISWANADHAM
Keyword(s):  
Analytic Continuation ◽  
Zeta Functions
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