Research on special values on L-functions of automorphic forms

自守形式L-函数特殊值的研究

• 批准号: 17540003
• 负责人: KATSURADA Hidenori
• 金额: $ 2.43万
• 依托单位: Muroran Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540003/
• 关键词: Standard zeta function; Ikeda lift; Congruenc of Siegel modular forms; Fourier-Jacobi coefficient; Rankin-elberg zeta function; Bloch-Kato conjecture; Harder's conjeture; Ikeda' conjecture; スタンダードL関数の中心でのnon-vanishing_; スタンダードL関数の中心点でのnon-vanishi

(1) We gave an explicit formula for a certain Dirichlet series of Rankin-Selberg type associated with the Fourier-Jacobi coefficients of the Ikeda lifting. (Joint work with. Kawamura (Hokkaido Univ.))(2) By using (1), we rewrote a conjecture concerning the period of the Ikeda lift proposed by T Ikeda in terms of the period of a certain half-integral weight Siegel modular forms. As a result we proved Ikeda's conjecture. (Joint work with. Kawamura (Hokkaido Univ.))(3) We proposed a conjecture, which related the congruence between the Ikeda lift of an elliptic modular from f and non-Ikeda lift with the special values of L-functions of f. By using (2) we proved our conjecture.(4) We gave a talk about (1), (2) and (3), for examples, on the following meetings ^*RI MS conference (2007,1.16), ^*The 52th Algebra Symposium (2007,8.7), ^*Special lecture at the annual meetings of M. S. J (2008,3.24)(5) We gave an exact values of the standard L-function of a certain vector valued Siegel modular forms, which is related with Harder's conjecture. (Joint work with T. Ibukiyama (Osaka Unuv.).(6) We investigate the non-vanishing of the central critical values of standard L-function of Siegel modular forms of degree 2 (Joint work with K. Matsumoto (Nagoya Univ.) and M. Chida (Tohoku Univ.))

(1)给出了一类与Ikeda举升的Fourier-Jacobi系数相关的Rankin-Selberg型Dirichlet级数的显式公式。与…共同工作。(2)利用(1)，我们用某半积分权Siegel模形式的周期改写了T Ikeda提出的关于Ikeda举升周期的猜想。结果证明了池田的猜想。与…共同工作。Kawamura (Hokkaido university))(3)我们提出了一个关于f的椭圆模的Ikeda举升和非Ikeda举升与f的l函数的特殊值之间的同余性的猜想。利用(2)证明了我们的猜想。(4)以(1)、(2)、(3)为例，在^*RI MS会议（2007,1.16）、^*第52届代数学术研讨会（2007,8.7）、^* M. S. J年会（2008,3.24）的专题讲座上作了讨论。(5)给出了与hard猜想有关的某向量值Siegel模形式的标准l函数的精确值。（与T. Ibukiyama（大阪大学）合作）。(6)研究了2次Siegel模形式的标准l函数的中心临界值的不消失性（与名古屋大学的K. Matsumoto和日本东北大学的M. Chida联合工作）。

项目成果

Extremal self-dual codes of length 64 throug and covering radii

长度为 64 的极值自对偶代码通过和覆盖半径

• 发表时间: 2007
• 期刊: Designs, Codes and Cryptography 42
• 作者: Naoki Chigira;Masaaki Harada and Masaaki Kitazume
• 通讯作者: Masaaki Harada and Masaaki Kitazume

On the basis problem for Siegel modular forms with level,

基于具有水平的 Siegel 模形式的基本问题，

• 期刊: Modular Forms on Schiermonnikoog (To appear)
• 作者: Juergen Herzog;Yukihide Takayama;Naoki Terai;H.Katsurada;Mutsumi Amasaki;H.Katsurada;H. Katsurada;Shoetsu Ogata;S. Boecherer;Atsushi Noma;M.Amasaki;H. Katsurada;S.Ogata;H. Katsurada and H. Kawamura;A.Noma;S. Boecherer
• 通讯作者: S. Boecherer

A proof of Ikeda's conjecture on the period of the Ikeda lift (Joint work with H. Kawamura)

池田关于池田电梯时期猜想的证明（与H. Kawamura 合作）

• 发表时间: 2008
• 作者: Juergen Herzog;Yukihide Takayama;Naoki Terai;H.Katsurada;Mutsumi Amasaki;H.Katsurada;H. Katsurada;Shoetsu Ogata;S. Boecherer;Atsushi Noma;M.Amasaki;H. Katsurada;S.Ogata;H. Katsurada and H. Kawamura;A.Noma;S. Boecherer;C.Miyazaki;桂田英典;N.Terai 他;宮崎 誓;H. Katsurada;宮崎誓;Chikashi Miyazaki;H. Katsurada
• 通讯作者: H. Katsurada

Siegel保型形式の周期と合同および関連する話題

西格尔模形式的周期和同余性及相关主题

• 发表时间: 2008
• 作者: 小松啓一;福田隆;池田保;T. Ibukiyama;Tomoyoshi Ibukiyama;T. Ibukiyama;Toraoyoshi Ibukiyama;雨宮 昭彦;T. Ibukiyama;三ツ石 郁夫(上川 孝夫と共編著);E. Bannai;Tomoyoshi Ibukiyama;柳澤 治;山崎 志郎;桂田英典
• 通讯作者: 桂田英典

Special values of the standard zeta functions for Elliptic modular forms

椭圆模形式的标准 zeta 函数的特殊值

• 发表时间: 2005
• 期刊: Experimental Mathematics 14 (To appear)
• 作者: H.Katsurada.