Periods and congruence of modular forms, and Selmer group

模形式的周期和同余，以及 Selmer 群

• 批准号: 21540004
• 负责人: KATSURADA Hidenori
• 金额: $ 2.91万
• 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: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540004/
• 关键词: 数論; 合同; Triple L関数; Ikeda-Miyawaki lift; Poincare級数; twisted Kocher-Maass級数; Rankin-Selberg級数; 1次従属性; スタンダードL関数; Ikeda lift; 保型形式の合同; Kim-Shahidi lift; エルミートモジュラー形式; Rankin-Selberg zeta関数; Ikeda予想; スタンダードゼータ関数; Harder予想; Bloch-Kato予想

(1) We solved Ikeda's conjecture on the period of the Hermitian Ikeda lift.(2) We compute the special values of ceratain vector valued Siegel modular forms and confirmed a conjecture proposed by N. Dummigan (joint work with N. Dummigan and T. Ibukiyama). Moreover we computed the special values of the standard L-function of the Kim-Shahidi lift of Ramanujan delta function △, and confirmed that it is complatible with Zagier's conjecture on the special values of symmetric forth L function of △(joint work with T. Ibukiyama).(3) We established an algorithm for computing the special values of the triple L function of elliptic modular forms (joint work with T. Ibukiyama). By using it we considered the congruence between Ikeda-Miyawaki lift and non- Ikeda-Miyawaki lift (joint work with T. Ibukiyama, C. Poor, and D. Yuen).(4) We gave an explicit formula for the Fourier coefficient of the Poincare series for the congruence subgroup Γ_0 (N) of S_<p2>(Z).(5) We gave an explicit formula of twisted Koecher-Maass series of the Saito-Kurokawa lift. As an application we obtained a linear dependence of the special values of the Rankin-Selberg series of certain half-integral weight modular forms (joint work with Y. Mizuno). Moreover we gave an explicit formula of twisted Koecher-Maass series of the Duke-Imamoglu-Ikeda lift.(6) We consider congruence between the Klingen-Eisenstein series and cups forms (joint work with S. Mizumoto).

(1)求解了池田关于池田升降周期的猜想。(2)我们计算了某些向量值Siegel模形式的特殊值，并证实了N. Dummigan（与N. Dummigan和T. Ibukiyama合作）提出的一个猜想。此外，我们还计算了Ramanujan函数△的Kim-Shahidi升力的标准L函数的特殊值，并证实了它与Zagier关于△的对称四维L函数的特殊值的猜想是相容的（与T. Ibukiyama合著）。(3)建立了椭圆模形式的三重L函数的特殊值的计算算法（与T. Ibukiyama合作）。通过使用它，我们考虑了池田-宫崎抬升和非池田-宫崎抬升之间的同余性（与T. Ibukiyama， C. Poor和D. Yuen共同研究）。(4)给出了S_<p2>(Z)的同余子群Γ_0 (N)的Poincare级数的傅里叶系数的显式表达式。(5)给出了齐藤-黑川隆起扭曲koecher - mass级数的显式公式。作为应用，我们得到了某些半积分权模形式的Rankin-Selberg级数的特殊值的线性依赖性（与Y. Mizuno合著）。并给出了Duke-Imamoglu-Ikeda隆起的扭曲koecher - mass级数的显式公式。(6)我们考虑了克林根-爱森斯坦级数和杯形之间的同余性（与S. Mizumoto的联合工作）。

项目成果

Periods and congruences of various lifs

各种生命的周期和一致性

• 发表时间: 2011
• 作者: K.Bannai;S.Kobayashi;T.Tsuji;H.Katsurada
• 通讯作者: H.Katsurada

Formal power series attached to Siegel series of Rankin Selberg tye related to Siegel series and its application to Siegel modular forms

兰金·塞尔伯格的西格尔级数的形式幂级数与西格尔级数相关的形式及其在西格尔模形式中的应用

• 发表时间: 2009
• 作者: K.Bannai;S.Kobayashi;T.Tsuji;H.Katsurada;滝口圭子・寺田容子・宮本昌子・五里江陽子・松為信雄;辻雄;H. Katsurada;宮本昌子・寺田容子・滝口圭子・五里江陽子・松為信雄;H.Katsurada;辻雄;庄司百合子・寺田容子・新堀和子・松為信雄;辻雄;H. Katsurada
• 通讯作者: H. Katsurada

Rankin Selberg method and periods of modular forms

Rankin Selberg 方法和模形式的周期

• 发表时间: 2010
• 期刊: MSJ Memoirs
• 作者: 久永 聡子;積山 薫;伊賀崎 伴彦;村山 伸樹;藤田昌久・吉川洋[編著];T. Kohno;H. Katsurada
• 通讯作者: H. Katsurada

An explicit formula for the twisted Kocher-Maass series of the Saito-Kurokawa lift and its applications

Saito-Kurokawa电梯扭曲Kocher-Maass级数的显式公式及其应用

• 发表时间: 2009
• 期刊: 京大数理研講究録
• 作者: S.-Y. Baek;F. Kaneda;M. Ozawa;K. Edamatsu;稲永由紀;A. Futaki;K. Ono;小林恵・大塚由美子・金沢創・山口真美・柿木隆介;桂田英典,水野義紀
• 通讯作者: 桂田英典,水野義紀

An Atkin-Lehner type theorem on Siegel modular forms Several Variables

关于 Siegel 模形式的 Atkin-Lehner 型定理形成多个变量

• 发表时间: 2011
• 期刊: Series on Number Theory and Its Applications
• 作者: T.Ibukiyama;H.Katsurada
• 通讯作者: H.Katsurada