Research on automorphic representations

自守表示研究

• 批准号: 06402001
• 负责人: YOSHIDA Hiroyuki
• 金额: $ 7.55万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06402001/
• 关键词: L-function; Lie group; period of an abelian variety; semisimple Lie群; 保型形式; 周期; 保型表現; モジュラー形式

H.Yoshida studied periods of Hilbert modular forms and proved Shimura's conjectures on P,Q-invariants. He also studied the derivatives of Artin's L-functions at s=0 and found a relation with periods of abelian varieties with complex multiplication. This relation can be sharpened by the notion of "absolute CM-periods".T.Ikeda studied residues of Eisenstein series and proved a Siegel-Weil type formula when Eisenstein series does not converge.K.Hiraga studied the multiplicity of a discrete series representation with which it occurs in L^2 (GAMMA/G), where G is a semisimple Lie group and GAMMA is a discrete subgroup.T.Umeda studied the notion of dual reductive pair in the case of quatum groups ; he generalized Capelli type identities for this case.H.Hijikata conjectured an approximation theorem for semisimple algebras over the quotient field of a Dedekind domain ; related with this conjecture, he obtained many results on orders and lattices.

H. Yoshida研究了希尔伯特模块化形式的时期，并证明了Shimura在P，Q-Invariants上的猜想。他还研究了S = 0的Artin L功能的衍生物，并发现了与带有复杂乘法的Abelian品种时期的关系。可以通过“绝对cm periods”的概念来提高这种关系。离散子组t.umeda研究了quatum组的双重还原对的概念。他对这种情况进行了广泛的capelli类型身份。与这个猜想有关，他在订单和格子上获得了许多结果。

项目成果

H.Hijikata: "On-the decemposilion of lattices over orders" Journal of Math.Soc.Japan. 49-3(発表予定).

H. Hijikata：“On-the deemposilion oflattice over order”Journal of Math.Soc.Japan 49-3（待出版）。

H. Yoshida: "On a conjecture of Shimura concrning periods of Hilbcrt modular farms" Amer, J. Math.117. 1019-1038 (1995)

H. Yoshida：“关于 Shimura 关于 Hilbcrt 模块化农场时期的猜想”Amer，J. Math.117。

H. Yoshida: "On calculations of zeros of various L-funcrtions" Journal of Mathematics of Kyoto University. 35. 663-696 (1995)

H. Yoshida：“关于各种 L 函数的零点的计算”京都大学数学杂志。

Takeshi Hirai: "Representations of Diffeomorphism groups and the intinite symmetric group" Noncompact Lie groups and some of their applications(Kluwer). 225-237 (1994)

Takeshi Hirai：“微分同胚群和无限对称群的表示”非紧李群及其一些应用（Kluwer）。

Tamotsu Ikeda: "On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstem serie" Journal of Mathematics of Kyoto University. 34. 615-636 (1994)

池田保：“论Eisenstem系列的雅可比形式和傅里叶-雅可比系数的理论”京都大学数学杂志。