Rankin–Cohen brackets on Siegel modular forms and special values of certain Dirichlet series

2016 ◽  
Vol 44 (1) ◽  
pp. 63-73 ◽  
Author(s):  
Abhash Kumar Jha ◽  
Brundaban Sahu
Keyword(s):  
Dirichlet Series ◽  
Modular Forms ◽  
Siegel Modular Forms ◽  
Special Values

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.

scholarly journals On the Spezialschar of Maass

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Bernhard Heim
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Special Values ◽  
Direct Sum

Let be the space of Siegel modular forms of degree and even weight . In this paper firstly a certain subspace Spez the Spezialschar of , is introduced. In the setting of the Siegel threefold, it is proven that this Spezialschar is the Maass Spezialschar. Secondly, an embedding of into a direct sum Sym2is given. This leads to a basic characterization of the Spezialschar property. The results of this paper are directly related to the nonvanishing of certain special values of L-functions related to the Gross-Prasad conjecture. This is illustrated by a significant example in the paper.

scholarly journals On Dirichlet Series and Petersson Products for Siegel Modular Forms

2008 ◽  
Vol 58 (3) ◽  
pp. 801-824 ◽  
Author(s):  
Siegfried Böcherer ◽  
Francesco Ludovico Chiera
Keyword(s):  
Dirichlet Series ◽  
Modular Forms ◽  
Siegel Modular Forms
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