The special values of the L function associated with automorphic forms

(1)在本研究中，我们改进了以往关于杯型之间关系的结果。为精确起见，我们证明了任意权的本原尖点形式的存在性，它与与二次数域的射线类性质有关的权1的本原尖点形式相同。这一结果是1981年证明的前人定理的推广。证明的关键是对广义Bernoulli数的研究。新证明了与Bernoulli数有关的一些积分性质。这种本原性是前人研究的结果。(2)对于足够一般的域，Hecke算子在全实数域上的Hilbert尖点形式空间中的本征值的计算是失败的。因此，对合理的结构进行了研究。新增加了黑克场和扭伴随L函数的特例，支持了Doi-Hida-Ishii的猜想。数学课。1998(3)T.Kagawa确定了定义在处处有良好约化或小导体的二次数域上的椭圆曲线。(4)O.Yamada给出了关于Dirac算子本质自正性的一些结果。

(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.