Arithmetic invariants and automorphic L-functions for automorphic forms of several variables

多个变量自同构形式的算术不变量和自同构 L 函数

• 批准号: 23540033
• 负责人: MURASE Atsushi
• 金额: $ 3.24万
• 依托单位: Kyoto Sangyo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 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-23540033/
• 关键词: 保型形式; 代数群; Borcherds lift; 対称性; テータリフト; フーリエ展開; 保型L関数; Borcherds積; L関数; 周期; 国際研究者交流; ドイツ:オマーン; 多変数保型形式; ドイツ：オマーン

We investigated arithmetic properties of Arakawa lifts, which are automorphic forms on the unitary group of degree two for a quaternion algebra over the rational number field constructed via theta lifting. In particular we obtained a formula for the square of the absolute value of a certain average of Fourier coefficients of an Arakawa lift in terms of special values of automorphic L-functions.We characterize the holomorphic Borcherds lifts on orthogonal groups of quadratic forms of signature (2, n+2) in terms of the multiplicative symmetries. We also showed that a similar fact holds for Jacobi forms.

我们研究了由theta提升构造的有理数域上的Arakawa提升的算术性质，它是四元数代数的二次酉群上的自同构形式。特别地，我们利用自同构L函数的特定值得到了Arakawa提升的傅里叶系数的某个平均值的绝对值的平方公式，并利用乘法对称性刻画了符号(2，n+2)的二次型正交群上的全纯Borcherds提升.我们还证明了类似的事实也适用于雅可比形式。

项目成果

Borcherds lifts on Sp_2(Z), "Geometry and Analysis of Automorphic Forms of Several Variables"

Borcherds 在 Sp_2(Z) 上的提升，“多变量自守形式的几何与分析”

• 发表时间: 2011
• 期刊: Proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60-th birthday, World Scientific to appear
• 作者: B.Heim;A.Murase
• 通讯作者: A.Murase

Igusa's modular form

Igusa 的模块化形式

• 发表时间: 2011
• 作者: B. Heim;A. Murase;Atsushi Murase and Bernhard Heim;Shin-ya Koyama and Nobushige Kurokawa;A. Murase;Shin-ya Koyama and Sachiko Nakajima;A. Murase;小山信也;B. Heim and A. Murase;Shin-ya Koyama and Nobushige Kurokawa;B. Heim and A. Murase;Shin-ya Koyama and Nobushige Kurokawa;B. Heim and A. Murase
• 通讯作者: B. Heim and A. Murase

Symmetries for Siegel theta functions, Borcherds lifts and automorphic Green functions

西格尔 theta 函数、Borcherds 提升和自同构格林函数的对称性

• 发表时间: 2013
• 期刊: J. Number Theory
• 作者: B. Heim;A. Murase
• 通讯作者: A. Murase

A characterization of Borcherds lifts by symmetries

通过对称性描述 Borcherds 升力

• 发表时间: 2011
• 作者: B. Heim;A. Murase;Atsushi Murase and Bernhard Heim;Shin-ya Koyama and Nobushige Kurokawa;A. Murase;Shin-ya Koyama and Sachiko Nakajima;A. Murase;小山信也;B. Heim and A. Murase
• 通讯作者: B. Heim and A. Murase

Geometry and Analysis of Automorphic Forms of Several Variables

多变量自守形式的几何与分析

• 发表时间: 2011
• 作者: Y. Hamahata;T. Ichikawa;A. Murase and T. Sugano
• 通讯作者: A. Murase and T. Sugano