Automorphic forms and L functions on algebraic groups

代数群上的自守形式和 L 函数

• 批准号: 09640040
• 负责人: SUGANO Takashi
• 金额: $ 1.98万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640040/
• 关键词: automorphic form; L function; Shintani function; Weil representation; theta function; テ-タ関数; 保型表現

1. Automorphic L-functions on unitary groups (joint work with A.Murase)We poved the analytic continuation and the functional equations of the standard L-function associated with a holomorphic cusp form on a unitary group. The key ingredient in the proof is a study of Shintani functions.2. Automorphic forms on unitary groups of degree 3 and primitive theta functions (joint work with A.Murase)For the study of arithmetical automorphic forms on a unitary group of degree 3, primitive theta functions are fundamental. We investigated a metaplectic representation of U(1) acting on the space of local primitive theta functions and gave its explicit irreducible decomposition.As an application, we determined the refined Fourier-Jacobi expansion of holomorphic Eisenstein series.3. theta lift and Jacobi group (joint work with A.Murase)Since Kudla lift is a restriction of Oda lift, we can construct automorphic forms on unitary groups of degree 3 from Jacobi forms explicitly. We gave another formulation of refined Fourier-Jacobi expansion of holomorphic Eisenstein series using Jacobi type Eisenstein series.

1。对单位组的自动形态L功能（与A.murase的联合工作）我们介绍了与单位组上与霍明型尖端形式相关的标准L功能的分析延续和功能方程。证明的关键成分是对Shintani功能的研究2。统一学位和原始theta功能（与A.Murase的联合工作）的统一组的自态形式用于研究算术自动形式的算法3级，这是基本的theta函数。我们研究了作用于局部原始theta函数空间的U（1）的元代表，并给出了其明确的不可约解的分解。作为应用，我们确定了精致的傅立叶雅各比扩张的Holomorphic Eisenstein系列。3。 Theta Lift和Jacobi Group（与A.Murase的联合工作）由于Kudla升力是ODA提升的限制，因此我们可以明确地从Jacobi形式的3级统一组上构建自动形式。我们使用Jacobi型Eisenstein系列的艾森斯坦系列的精致傅里叶 - 雅各比膨胀进行了另一种表述。

项目成果

A.Murase and T.Sugano: "On standard L-functions attached to automorphic forms on orthogonal groups" Nagoya Math.J.152. 57-96 (1998)

A.Murase 和 T.Sugano：“关于附加到正交群上自守形式的标准 L 函数”Nagoya Math.J.152。

H.Ishibashi: "Terwilliger algebras of cyclotomic schemes and Jacobi sum." European Journal of Combinatorics. in print.

H.Ishibashi：“分圆方案的特威利格代数和雅可比和。”

S.Hobart: "The structure of Nonthin Iweducible F-modules of Endpoint 1:Ladder Bases and Classical Parameters" Journal of Algebraic. (to appear in).

S.Hobart：“端点 1 的非薄可解 F 模的结构：阶梯基和经典参数”代数杂志。

A.Murase: "On Standard L-functions attached to automcrphic forms on definite of Hiogonal groups" Nagoya Math. J.152. 57-96 (1998)

A.Murase：“关于附加到 Hiogonal 群确定的自自形式的标准 L 函数”名古屋数学。

H.Ishibashi: "Terwilliger algebras of cyclotomic schemes and Jacobisums." European Journal of Combinatorics. in print.

H.Ishibashi：“分圆方案和雅可比和的特威利格代数。”