scholarly journals Special values of zeta functions attached to Siegel modular forms

1981 ◽  
Vol 14 (1) ◽  
pp. 77-120 ◽  
Author(s):  
Michael Harris
Keyword(s):  
Modular Forms ◽  
Zeta Functions ◽  
Siegel Modular Forms ◽  
Special Values

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.

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