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

@article{Takase1986OnTT,
  title={On the trace formula of the Hecke operators and the special values of the second L-functions attached to the Hilbert modular forms},
  author={Koichi Y. Takase},
  journal={manuscripta mathematica},
  year={1986},
  volume={55},
  pages={137-170}
}
  • K. Takase
  • Published 1 June 1986
  • Mathematics
  • manuscripta mathematica
In this paper, we consider 1) the explicit formula of the trace of the Hecke operators acting on the space of the Hilbert cusp forms, and 2) the special values of the second L-functions attached to the Hilbert cusp forms. The method is that of Zagier[12], and the results of this paper are the generalization of his results to the case of the Hilbert modular forms for the congruence subgroup Γ0 (M). 
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本記事では,あるテスト関数 fの積分核の対角成分への制限 K1(g,g)とevenな Hecke-Maassカスプ形式中の積の積分を考察することによって得られた "<pの重みつき跡公 式”について解説する.得られた公式の応用として, evenなHecke-Maassカスプ形式 fに対し て, L(l/2,fx F)が非ゼロになるような GL3のコホモロジカル Hecke固有形式 Fが無限に
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References

SHOWING 1-10 OF 10 REFERENCES
On Automorphic Forms on GL 2 and Hecke Operators
In [4], Jacquet and Langlands showed that if an irreducible unitary representation of the general linear group of degree 2 over the adele ring of an A-field' is an irreducible constituent of the
Automorphic forms and algebraic extensions of number fields, II
§ 0. The purpose of this paper is to present a result on an arithmetical relation between Hilbert cusp forms over a totally real algebraic number field, which is a cyclic extension of the rational
ON DISCONTINUOUS GROUPS OPERATING ON THE PRODUCT OF THE UPPER HALF PLANES
Let H" be the direct product of the n upper half planes, and let G be the connected component of the identity of the group of all analytic automorphisms of Hn. G is the direct product of n subgroups
Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 57 Chapter 1 : The Intersection Behaviour of the Curves T N . . . . . . 60 1.1. Special Points . . . . . . . . . . . . . . . . . . . . .
Über den bizyklischen biquadratischen Zahlkörper
Unter einem bizyklischen biquadratischen Zahlkorper verstehen wir einen absolut abelschen Zahlkorper vierten Grades, der von zwei verschiedenen quadratischen Zahlkorpern zusammengesetzt wird. Wir