On Zeta Functions Associated to the Product of Two Eisenstein Series

2017 ◽  
pp. 131-161
Author(s):  
Bradford Lyon
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions

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.

scholarly journals Multiple Dedekind zeta functions

2017 ◽  
Vol 2017 (722) ◽  
Author(s):  
Ivan Emilov Horozov
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Quadratic Fields ◽  
Multiple Zeta Values ◽  
Imaginary Quadratic Fields ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Zeta Values ◽  
New Type

AbstractIn this paper we define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider MDZV as a number theoretic generalization of Euler’s multiple zeta values. Over imaginary quadratic fields MDZV capture, in particular, multiple Eisenstein series [

scholarly journals Hecke’s Integral Formula for Relative Quadratic Extensions of Algebraic Number Fields

2008 ◽  
Vol 189 ◽  
pp. 139-154 ◽  
Author(s):  
Shuji Yamamoto
Keyword(s):  
Zeta Function ◽  
Eisenstein Series ◽  
Algebraic Number ◽  
Integral Formula ◽  
Zeta Functions ◽  
Quadratic Extension ◽  
Number Fields ◽  
Algebraic Number Fields ◽  
Limit Formula ◽  
Quadratic Extensions

AbstractLet K/F be a quadratic extension of number fields. After developing a theory of the Eisenstein series over F, we prove a formula which expresses a partial zeta function of K as a certain integral of the Eisenstein series. As an application, we obtain a limit formula of Kronecker’s type which relates the 0-th Laurent coefficients at s = 1 of zeta functions of K and F.

Eisenstein series and zeta functions on symplectic groups

1995 ◽  
Vol 119 (1) ◽  
pp. 539-584 ◽  
Author(s):  
Goro Shimura
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Symplectic Groups
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