The special values of the L function associated with automorphic forms

与自守形式相关的 L 函数的特殊值

• 批准号: 12640049
• 负责人: ISHII Hidenori
• 金额: $ 1.47万
• 依托单位: Ritsumeikan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640049/
• 关键词: Automorphic forms; L-function; Hilbert cusp forms; Hilbert cusp forms

(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.

(1)在本研究中，我们改进了以往关于杯形之间关系的结果。确切地说，我们证明了任意权的本原尖点形式的存在性，该形式与与二次数域的射线类特征相关的权1的尖点形式全等。这个结果是1981年证明的一个定理的推广.证明的关键是对广义Bernoulli数的研究。证明了与Bernoulli数有关的一些可积性性质。这是前人研究的结果。(2)在充分一般的域上，计算全真实的数域上Hilbert尖点型空间中Hecke算子的本征值是不可能的.为此，对合理结构进行了研究。新增加了Hecke场和扭曲伴随L函数的特殊值的数值例子，支持了发明人Doi-Hida-石井的猜想. math.1998（3）定义在二次数域上处处具有好约化或小导体的椭圆曲线由T.香川。(4)O. Yamada给出了Dirac算子的本质自相关性的一些结果。

项目成果

加川 貴章: "Determination of elliptic curves with everywhere good reduction over real quadratic fields Q(√<3p>)"Acta Arith.. 96. 231-245 (2001)

Takaaki Kakawa：“实二次域 Q(√<3p>) 上处处良好归约的椭圆曲线的确定”Acta Arith.. 96. 231-245 (2001)

山田 修宣: "Essential self-adjointness of Dirac operators with a variable mass term"Proc.of Japan Acad.. 76. 13-15 (2000)

Nobunobu Yamada：“具有变质量项的狄拉克算子的基本自伴性”Proc.of Japan Acad.. 76. 13-15 (2000)

山田 修宣: "Essential self-adjointness of n-dimensional Dirac operators with a variable mass term"J.of Mathematical Physics. 42. 2667-2676 (2001)

Nobunobu Yamada：“具有变质量项的 n 维狄拉克算子的本质自伴性”J.of 数学物理。 42. 2667-2676 (2001)

加川貴章: "Determination of elliptic curves with everywhere good reduction over real quadratic fields Q(√<3p>)"Acta Arith.. 96. 231-245 (2001)

Takaaki Kakawa：“实二次域 Q(√<3p>) 上处处良好归约的椭圆曲线的确定”Acta Arith.. 96. 231-245 (2001)

Takaaki Kagawa: "Determination of elliptic curves with everywhere good reduction over real quadratic fields Q(√<3p>)"Acta Arith.. 96. 231-245 (2001)

Takaaki Kakawa：“实二次域 Q(√<3p>) 上处处良好归约的椭圆曲线的确定”Acta Arith.. 96. 231-245 (2001)