Zeta functions of prehomogeneous vector spaces and automorphic distributions

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400021
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba Institute of Technology
• Principal Investigator: Sugiyama Kazunari 千葉工業大学, 情報科学部, 准教授 (90375395)
• Co-Investigator(Renkei-kenkyūsha): Sato Fumihiro 立教大学, 名誉教授 (20120884)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 概均質ベクトル空間 / ゼータ関数 / 保型超関数 / 実解析的保型形式 / 国際研究者交流（フランス）

Outline of Final Research Achievements

We have studied automorphic distributions. We have proved a converse theorem by which one can construct automorphic distributions for congruence subgroups from L-functions with functional equations, and by using the Poisson transform, we have established a method to construct real analytic automorphic forms for congruence subgroups from L-functions. Moreover, we have confirmed that a certain prehomogeneous zeta function with 2 variables, which has been studied by Takahiko Ueno, satisfies the assumption of our converse theorem. This gives Maass forms whose coefficients are the number of the solutions of quadratic congruence equations.

Free Research Field

代数学