Arithmeticity of the critical values of zeta functions and Eisenstein series of general types

2010 ◽  
pp. 219-246
Author(s):  
Goro Shimura
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Critical Values

scholarly journals On generalized Eisenstein series and Ramanujan’s formula for periodic zeta-functions

2017 ◽  
Vol 184 (1) ◽  
pp. 77-103
Author(s):  
M. Cihat Dağlı ◽  
Mümün Can
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Ramanujan’S Formula

scholarly journals Zeta functions and Eisenstein series on classical groups

1997 ◽  
Vol 94 (21) ◽  
pp. 11133-11137 ◽  
Author(s):  
G. Shimura
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Classical Groups

Algebraic relations between critical values of zeta functions and inner products

2003 ◽  
pp. 422-454
Author(s):  
Goro Shimura
Keyword(s):  
Zeta Functions ◽  
Critical Values ◽  
Inner Products

scholarly journals Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and q-zeta functions

2014 ◽  
Vol 26 (4) ◽  
Author(s):  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Hurwitz Numbers ◽  
Hyperbolic Sine

scholarly journals Zeta functions on tori using contour integration

2015 ◽  
Vol 12 (02) ◽  
pp. 1550019
Author(s):  
Emilio Elizalde ◽  
Klaus Kirsten ◽  
Nicolas Robles ◽  
Floyd Williams
Keyword(s):  
Functional Equation ◽  
Eisenstein Series ◽  
Zeta Functions ◽  
Contour Integration ◽  
Alternative Proof ◽  
Functional Determinant ◽  
Dedekind Eta Function ◽  
Limit Formula ◽  
Complex Tori ◽  
The One

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla–Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

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