Studies on arithmetic automorphic forms and zeta functions

算术自守形式和zeta函数的研究

• 批准号: 09440025
• 负责人: MURASE Atsushi
• 金额: $ 5.06万
• 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 (B)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440025/
• 关键词: automorphic forms; algebraic group; Fourier-Jacobi expansion; metaplectic representation; Heisenberg goup; automorphic L-function; theta lift; Howe correspondence; Fourier-Jacobi展開; Metaplectic表現; Heisenberg群; 多変数保型形式; ユニタリ群; metaplectic repr

(6) A New splitting of metaplectic representations of unitary groups and a simple proof of Howe's character formulaIn this research project, we studies automorphic forms on unitary groups, in particular their arithmeticity, and related representation theory of algebraic groups over local fields. Our main results, which are joint works with T.Sugano except 6, are summarized as follows.(1) A New simple proof and refinement of epsilon dichotomy for U(1)(2) Adelic reformulation and refiment of the theory of Fourier-Jacobi expansion of automorphic forms on U(2,1) originally due to T.Shintani(3) Explicit calculation of Fourier-Jacobi expansion of holomorphic Eisenstein series on U(2,1)(4) A criterion for the non-vanishing of Fourier-Jacobi expansion of holomorphic Eisenstein series on U(2,1) in terms of the critical central values of Hecke L-functions(5) Adelic reformulation of Kudla lift

(6)酉群的亚代数表示的一种新的分裂和Howe特征标的一个简单证明本研究课题主要研究酉群上的自守形式，特别是它们的算术性，以及局部域上代数群的相关表示理论。我们的主要结果，其中除了6是与T.Sugano合作工作，总结如下。(1)U（1）的一个新的简单证明和二分性的改进（2）T.Shintani关于U（2，1）上自守形式的Fourier-Jacobi展开理论的Adelic重新表述和改进（3）U（2，1）上全纯Eisenstein级数的Fourier-Jacobi展开的显式计算（4）U（2，1）上全纯Eisenstein级数的Fourier-Jacobi展开的非零性的一个判据1）关于Hecke L-函数的临界中心值（5）Kudla升力的Adelic变换

项目成果

Murase,A., Sugano,T.: "On standard L-functions at tached to automorphic forms on definite orthogoual groups" Nagoya Mathematieal Journal. (to appear).

Murase,A.，Sugano,T.：“关于确定正交群上自守形式的标准 L 函数”名古屋数学杂志。

Ishida, H.: "Extremal length and the conformal imebeddings of plane regions"Acta. Human. Sci. Univ. Sangio Kyotiensis. 27. 15-23 (1998)

Ishida, H.：“平面区域的极值长度和共形 imebeddings”Acta。

Ishida: "Reduced extremal length and conformal imbeddings of plane regions"Acta. Human. Sci. Univ. Sangio Kyotiensis. 28. (1999)

Ishida：“减少极值长度和平面区域的保形嵌入”Acta。

H. Ishida: "Reduad extremal leugth and cenformal inbeddings of plane regious into disks"Acta Human, Sci, Univ. Sangio Kyotiensis. 28. 1-9 (1999)

H. Ishida：“将平面区域的极值长度和中心形式嵌入到磁盘中”Acta Human，Sci，Univ。

Mizuhara, A.: "Some examples of Hessian manifolds of constant sectional curvature and their automorphisms"Math.Japonica. 50. 169-177 (1999)

Mizuhara, A.：“恒定截面曲率的 Hessian 流形及其自同构的一些示例”Math.Japonica。