Study on arithmetic invariants attached to automorphic forms

自守形式算术不变量的研究

• 批准号: 18540057
• 负责人: MURASE Atsushi
• 金额: $ 2.5万
• 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: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540057/
• 关键词: automorphic form; Fourier coefficients; automorphic L-function; theta lift; period; algebraic group; automorphic form; Fourier coefficients; automorphic L-function; theta lift; period; algebraic group

(1) For an elliptic cusp form f on a Hecke congruence subgroup and a Hecke character W of an imaginary quadratic field K, I showed that the square of a xertain CM-period attached to (f,W) is expressed in terms of the central value of the L-function attached to (f,W), when the level off is square free.(2) We proposed a conjecture concerning a relation between the Fourier-Jacobi coefficients of a cusp form F on U(2,1) and the central values of automorphic L-functions attaced to F. The conjecture are proved when F is a holomorphic Eisenstein series or a unitary Kudla lift. The results in (1) are essentially used in the proof of the latter result. This is a joint work with Takashi Sugano.(3) Let f and f' be automorphic forms on GL(2) and the multiplicative group of a quaternion algebra B, respectively. Let L(f,f') be the theta lift on Sp(1,1) constructed from (f,f'). We showed that L(f,f') is a Hecke eigenform if so are f and f'. We also showed that the Fourier coefficients of L(f,f') are expressed in terms of CM-periods of f and f'. This is a joint work with Hiro-aki Narita.(4) A p-adic infinite family of Hilbert modular forms parameterized by an Affinoid Hecke variety is constructed. When the degree of the base field F is even, a p-adically analytic infinite family of Hilbert Hecke eigenforms of a fixed finite slope parameterized by weights is constructed. This is a work of Atsushi Yamagami.

（1）对于Hecke一致性亚组的椭圆形尖端形式F和一个假想的二次二次场K的hecke特征，我表明，与（f，w）附加的x ex period的平方表示，在（f，w）中附加了l-function的中心价值（f，w）的中心价值，当时clucked neveling claste never conterne cluss nevient conterne conters nefe and n s a n sare（2）我们（2）我们（2）我们（2）我们（2）我们（2）。 u（2,1）上尖的尖端jacobi系数和对F上的自动形态L功能的中心值。当F是f是h holomorphic eisenstein系列或统一的kudla升力时，证明了猜想。 （1）中的结果基本用于后一个结果的证明。这是与takashi sugano的共同作品。（3）令F和F'为GL（2）和四元组代数B的乘法组的自动形式。令L（f，f'）为sp（1,1）上（f，f'）上的theta升力。我们表明，如果是f和f'，则L（f，f'）是Hecke特征形式。我们还表明，L（f，f'）的傅立叶系数是用F和F'的CM-周期表示的。这是与Hiro-Aki Narita的联合作品。（4）建造了由affinoid Hecke品种参数化的Hilbert模块化形式的P-Adic Infinite家族。当基本F的程度均匀时，构建了由权重参数参数的固定有限斜率的Hilbert Hecke特征形式的P-Autialtion分析性无限家族。这是Atsushi Yamagami的作品。