MODULAR FORMS AND DIRICHLET SERIES

1971 ◽  
Vol 3 (1) ◽  
pp. 107-108
Author(s):  
Joseph Lehner
Keyword(s):  
Dirichlet Series ◽  
Modular Forms

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

Mixed Siegel Modular Forms and Special Valuesof Certain Dirichlet Series

2000 ◽  
Vol 131 (2) ◽  
pp. 109-122 ◽  
Author(s):  
YoungJu Choie ◽  
Min Ho Lee
Keyword(s):  
Dirichlet Series ◽  
Modular Forms ◽  
Siegel Modular Forms

scholarly journals A Dirichlet series for modular forms of degree n

1991 ◽  
Vol 59 (3) ◽  
pp. 243-259 ◽  
Author(s):  
Aloys Krieg
Keyword(s):  
Dirichlet Series ◽  
Modular Forms

Hecke's Theory of Modular Forms and Dirichlet Series

10.1142/6438 ◽  
2007 ◽  
Author(s):  
Bruce C Berndt ◽  
Marvin I Knopp
Keyword(s):  
Dirichlet Series ◽  
Modular Forms

scholarly journals Dirichlet series in the theory of Siegel modular forms

1984 ◽  
Vol 95 ◽  
pp. 73-84 ◽  
Author(s):  
Yoshiyuki Kitaoka
Keyword(s):  
Dirichlet Series ◽  
Eisenstein Series ◽  
Half Space ◽  
Modular Forms ◽  
Fourier Expansion ◽  
Siegel Modular Forms

We are concerned with Dirichlet series which appear in the Fourier expansion of the non-analytic Eisenstein series on the Siegel upper half space Hm of degree m. In the case of m = 2 Kaufhold [1] evaluated them. Here we treat the general cases by a different method.

Dirichlet Series and Modular Forms

2016 ◽  
pp. 105-133
Author(s):  
M. Ram Murty ◽  
Michael Dewar ◽  
Hester Graves
Keyword(s):  
Dirichlet Series ◽  
Modular Forms
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