On automorphic forms on algebraic groups: Arithmetic invariants and automorphic L-functions

关于代数群的自同构：算术不变量和自同构 L 函数

• 批准号: 20540031
• 负责人: MURASE Atsushi
• 金额: $ 2.83万
• 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: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540031/
• 关键词: 代数群; 保型形式; フーリエ展開; 保型L関数; 対称性; ボーチャーズ積; Borcherdsリフト; 積対称性; 四元数環; テータリフト; 国際研究者交流; オマーン; ジーゲル・テータ級数; ヒルベルトモジュラー形式; Borcherds積; ヘッケ作用素

Several invariants are attached to automorphic forms on algebraic groups. These invariants and relationships between them are very useful for studying the internal structure of automorphic forms. In this research, we investigated relationships between these invariants for automorphic forms of special kind called Aarkawa liftings. Using this result, we proposed certain conjectures on relations between invariants attached to automorphic forms on certain groups. We showed that automorphic forms called Borcherds products have strong symmetries (the multiplicative symmetries). We also studied the Borcherds products in detail in the genus two Siegel modular case. In particular, we obtained several results about the weights and characters of Borcherds products.

代数群上的自守形式附加了几个不变量。这些不变量以及它们之间的关系对于研究自同构形式的内部结构非常有用。在这项研究中，我们研究了称为 Aarkawa 提升的特殊自守形式的这些不变量之间的关系。利用这个结果，我们对某些群上自同构形式所附加的不变量之间的关系提出了某些猜想。我们证明了称为 Borcherds 乘积的自守形式具有很强的对称性（乘法对称性）。我们还在属二个Siegel模块化案例中详细研究了Borcherds产品。特别是，我们获得了有关 Borcherds 产品的重量和特性的一些结果。

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

Commutation relations of Heckeoperators for Arakawa lifting

荒川提升的 Hecke 算子的交换关系

• 发表时间: 2008
• 期刊: Tohoku J.Math. 60
• 作者: A.Murase;H.Narita
• 通讯作者: H.Narita

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

On recurrence relations and functional equations of infinite products

关于无限乘积的递推关系和函数方程

• 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
• 通讯作者: B. Heim and A. Murase

Fourier expansion of Arakawa lifting I : An explicit formula and examples of non-vanishing lifts

荒川提升 I 的傅立叶展开：非消失提升的显式公式和示例

• 发表时间: 2012
• 期刊: Israel Journal of Mathematics
• 影响因子: 1
• 作者: A. Murase;H. Narita
• 通讯作者: H. Narita