Sutudy of modular forms by Koecher-Maass series

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800021
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: The University of Tokushima
• Principal Investigator: Mizuno Yoshinori 徳島大学, 大学院理工学研究部, 准教授 (30546388)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: ケッヒャー・マース級数 / Ｌ関数 / アイゼンシュタイン級数 / モジュラー形式 / カトック・サルナック対応 / 特殊値

Outline of Final Research Achievements

1. We study a kernel function of the twisted symmetric square L-function of elliptic modular forms, and compute several exact special values of the L-function. We also succeed to determine some special values of the convolution product of two Eisenstein series of half-integral weight. 2. We give a characterization of degree 2 Hermitian cusp forms by the growth of their Fourier coefficients. 3. We give an explicit form of genus character L-functions. As an application, we generalize the formula due to Hirzebruch-Zagier on the class number of imaginary quadratic fields in term of the continued fraction expansion. 4. We give analytic properties of the Koecher-Maass series of non-holomorphic Siegel-Eisenstein series. It turned out that the series has a relation with Weyl group multiple Dirichlet series. 5. Katok-Sarnak type result for the Eisenstein series on higher dimensional hyperbolic space is established.

Free Research Field

数学・代数学