On the trace formula of the Hecke operators and the special values of the second L-functions attached to the Hilbert modular forms

1986 ◽  
Vol 55 (2) ◽  
pp. 137-170 ◽  
Author(s):  
Koichi Takase
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Hecke Operators ◽  
Hilbert Modular Forms ◽  
Special Values ◽  
Hilbert Modular

scholarly journals ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS

2013 ◽  
Vol 56 (1) ◽  
pp. 57-63
Author(s):  
CRISTIAN VIRDOL
Keyword(s):  
Finite Order ◽  
Modular Forms ◽  
Number Fields ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Special Values ◽  
Finite Dimensional ◽  
Arbitrary Base ◽  
Hilbert Modular

AbstractIn this paper we generalize some results, obtained by Shimura, on the special values of L-functions of l-adic representations attached to quadratic CM-base change of Hilbert modular forms twisted by finite order characters. The generalization is to the case of the special values of L-functions of arbitrary base change to CM-number fields of l-adic representations attached to Hilbert modular forms twisted by some finite-dimensional representations.

scholarly journals An explicit trace formula of Jacquet–Zagier type for Hilbert modular forms

2018 ◽  
Vol 275 (11) ◽  
pp. 2978-3064
Author(s):  
Shingo Sugiyama ◽  
Masao Tsuzuki
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Hilbert Modular Forms ◽  
Hilbert Modular

scholarly journals HECKE OPERATORS ON HILBERT–SIEGEL MODULAR FORMS

2007 ◽  
Vol 03 (03) ◽  
pp. 391-420 ◽  
Author(s):  
SUZANNE CAULK ◽  
LYNNE H. WALLING
Keyword(s):  
Number Field ◽  
Modular Forms ◽  
Product Space ◽  
Fourier Coefficients ◽  
Siegel Modular Forms ◽  
Linear Operators ◽  
Hecke Operators ◽  
Hilbert Modular Forms ◽  
Linear Transformations ◽  
Hilbert Modular

We define Hilbert–Siegel modular forms and Hecke "operators" acting on them. As with Hilbert modular forms (i.e. with Siegel degree 1), these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert–Siegel forms (i.e. with arbitrary Siegel degree) we identify several families of natural identifications between certain spaces of modular forms. We associate the Fourier coefficients of a form in our product space to even integral lattices, independent of basis and choice of coefficient rings. We then determine the action of the Hecke operators on these Fourier coefficients, paralleling the result of Hafner and Walling for Siegel modular forms (where the number field is the field of rationals).

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