Periods of automorphic forms and distribution of average of special values of L-functions

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540033
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Sophia University
• Principal Investigator: TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
• Co-Investigator(Kenkyū-buntansha): TSUNOGAI Hiroshi 上智大学, 理工学部, 教授 (20267416)
• Co-Investigator(Renkei-kenkyūsha): MORIYAMA Tomonori 大阪大学, 大学院理学研究科, 准教授 (80384171)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: Ｌ関数特殊値 / 保型形式の周期 / 相対跡公式

Outline of Final Research Achievements

(1)We studied the product of central values of standard L-function and their quadratic twist(or its first derivative) associated with holomorphic Hilbert modular forms over a general totally real number field. We developed an explicit relative trace formula whose spectral side encodes such quantities and obtained several applications, which includ the equidistribution of Satake parameters of automorphic represnetations and explicit subconvex exponent of certain central L-values in the weight aspect.
(2) We studied the holomorphic scalar valued cusp forms on type IV bounded symmetric domain from the aspect of their Fourier coefficients. We proposed a good normalization of certain weighted average of Fourier coefficients, which is compatible to known normalizations of classical modular forms. We developed a certain summation formula whose spectral side encodes the square of the normalized Fourier coefficients and the central values of the standard L-functions.

Free Research Field

整数論