Lifting for Siegel modular forms of half-integral weight

半积分重物西格尔模块化形式的提升

• 批准号: 23740018
• 负责人: HAYASHIDA SHUICHI
• 金额: $ 2.08万
• 依托单位: Joetsu University of Education (2012-2013)Osaka University (2011)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740018/
• 关键词: ジーゲル・アイゼンシュタイン級数; マース関係式; 重さ半整数の保型形式; リフティング; Zharkovskaya's theorem; 保型形式; Fourier-Jacobi 展開; Maass 関係式; Ikeda lift; Ikeda-Miyawaki lift; Zharkovskaya の定理; 国際研究者交流; ヤコビ形式; ジーゲル保型形式; ヒルベルト保型形式; ドイツ; アメリカ

Modular forms are functions of complex variables which have nice transformation formula. So-called "liftings" are certain maps between the space of modular forms of several variables and "liftings" are useful to investigate the structure of the space of modular forms and the properties of the L-functions.In this study I obtained lifting maps from two elliptic modular forms to Siegel modular forms of half-integral weight of even degrees under the assumption that the constructed form does not vanish. To show the lifting I obtained a certain generalization of the Maass relation for Siegel modular forms of half-integral weight of even degrees.

模形式是复变函数，具有良好的变换公式。所谓的“提升”是多元模形式空间之间的映射，“提升”对于研究模形式空间的结构和L-函数的性质是有用的，本文在假设所构造的模形式不为零的条件下，得到了从两个椭圆模形式到偶数次半整权Siegel模形式的提升映射。为了证明提升，我得到了偶数度半整数权的西格尔模形式的马斯关系的某种推广。

项目成果

Generalized Maass relations and Miyawaki-Ikeda lifts

广义马斯关系和 Miyawaki-Ikeda 提升

• 发表时间: 2013
• 作者: Shuichi Hayashida;S. Hayashida;Shuichi Hayashida;林田秀一;林田秀一;S. Hayashida;S. Hayashida;S. Hayashida
• 通讯作者: S. Hayashida

Numerical examples of Euler factors of Siegel modular forms of half-integral weight of degree three

三阶半积分权重西格尔模形式的欧拉因子数值算例

• 发表时间: 2012
• 作者: Shuichi Hayashida;S. Hayashida;Shuichi Hayashida;林田秀一;林田秀一;S. Hayashida;S. Hayashida;S. Hayashida;林田秀一;S. Hayashida
• 通讯作者: S. Hayashida

Generalized Maass relations and Miyawaki-Ikeda lifts.

广义马斯关系和宫胁-池田升降机。

• 发表时间: 2013
• 作者: Shuichi Hayashida;S. Hayashida;Shuichi Hayashida;林田秀一;林田秀一;S. Hayashida;S. Hayashida;S. Hayashida;林田秀一
• 通讯作者: 林田秀一

次数2の重さ半整数ジーゲル保型形式へのリフティング

提升为 2 阶加权半整数西格尔模形式

• 发表时间: 2011
• 期刊: 第56回代数学シンポジウム報告集
• 作者: Shuichi Hayashida;S. Hayashida;Shuichi Hayashida;林田秀一;林田秀一
• 通讯作者: 林田秀一

Cohen type Eisenstein series of degree two and a relation among Fourier coefficients

二次科恩型爱森斯坦级数与傅里叶系数之间的关系

• 发表时间: 2011
• 作者: Shuichi Hayashida;S. Hayashida;Shuichi Hayashida;林田秀一;林田秀一;S. Hayashida;S. Hayashida;S. Hayashida;林田秀一;S. Hayashida;林田秀一;林田秀一;林田秀一;S. Hayashida
• 通讯作者: S. Hayashida