Research on special values on L-functions of automorphic forms

(1)给出了与Ikeda提升的Fourier-Jacobi系数相关的Rankin-Selberg型Dirichlet级数的一个显式公式。（共同工作。川村（北海道大学）(2)利用（1），我们用半整权Siegel模形式的周期改写了T Ikeda提出的关于Ikeda提升周期的猜想.结果证明了池田猜想。（共同工作。川村（北海道大学）(3)本文提出了一个猜想，它将f的椭圆模的Ikeda提升与非Ikeda提升的同余关系与f的L-函数的特殊值联系起来。通过使用（2），我们证明了我们的猜想。(4)例如，我们在以下会议上讨论了（1）、（2）和（3）：^*RI MS会议（2007，1.16），^* 第52届代数研讨会（2007，8.7），^* M. S. J（2008，3.24）（5）给出了与Harder猜想相关的一类向量值Siegel模形式的标准L-函数的精确值。（与T。Ibukiyama（Osaka Unuv.）. (6)研究了2次Siegel模形式的标准L-函数的中心临界值的非零性。松本（名古屋大学）和M. Chida（东北大学）

(1) We gave an explicit formula for a certain Dirichlet series of Rankin-Selberg type associated with the Fourier-Jacobi coefficients of the Ikeda lifting. (Joint work with. Kawamura (Hokkaido Univ.))(2) By using (1), we rewrote a conjecture concerning the period of the Ikeda lift proposed by T Ikeda in terms of the period of a certain half-integral weight Siegel modular forms. As a result we proved Ikeda's conjecture. (Joint work with. Kawamura (Hokkaido Univ.))(3) We proposed a conjecture, which related the congruence between the Ikeda lift of an elliptic modular from f and non-Ikeda lift with the special values of L-functions of f. By using (2) we proved our conjecture.(4) We gave a talk about (1), (2) and (3), for examples, on the following meetings ^*RI MS conference (2007,1.16), ^*The 52th Algebra Symposium (2007,8.7), ^*Special lecture at the annual meetings of M. S. J (2008,3.24)(5) We gave an exact values of the standard L-function of a certain vector valued Siegel modular forms, which is related with Harder's conjecture. (Joint work with T. Ibukiyama (Osaka Unuv.).(6) We investigate the non-vanishing of the central critical values of standard L-function of Siegel modular forms of degree 2 (Joint work with K. Matsumoto (Nagoya Univ.) and M. Chida (Tohoku Univ.))