The special values of the L function associated with automorphic forms

点击翻译按钮获取中文摘要

(1) In this research, we improved the previous results which concern between cups forms. To be precise, we prove the existence of primitive cusp form of arbitrary weight which is congruent to the cusp form of weight one which associated with ray class character of quadratic number field. This result is a generalization of previous theorem which is proved m 1981. Key of the proof is a study of the generalized Bernoulli numbers. Some integrality properties which concern with the Bernoulli numbers are newly proved. The primitivity is a result of previous research.(2) Calculations of the eigenvalues of the Hecke operators in the space of Hilbert cusp forms over totally real number fields is died for sufficiently general fields. Therefore, the rational structure is studied. Numerical examples of the Hecke fields and the special values of twisted adjoin L functions are newly added which supports the conjecture of Doi-Hida-Ishii in invent. math. 1998(3) Elliptic curves defined over some quadratic number fields with everywhere good reduction or small conductor are determined by T. Kagawa.(4) O. Yamada give some results about the essential self-adointness of the Dirac operators.