Arithmetic of automorphic forms, an extension of its researching field in terms of explicit constructions

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540025
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kumamoto University
• Principal Investigator: NARITA Hiro-aki 熊本大学, 自然科学研究科, 准教授 (70433315)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 5次元双曲空間 / マース保型形式 / リフティング / ラマヌジャン予想 / 保型L関数の中心値 / 超幾何関数 / 例外型リー群

Outline of Final Research Achievements

The theory of automorphic forms, which is my reserach object, has been playing a crucial role in the number theroy as the achievements of the Langlands program indicate. The aim of this research is to deepen researches on automorphic forms in terms of their explicit construction. I have obtained two results: One is to provide explicit construction of automorphic forms which are counterexamples of the Ramanujan conjecture, and another one is a result on the non-vanishing of the central values of some automorphic L-functions in terms of special values of certain hypergeometric functions, whose origin does not come from the number theory.

Free Research Field

代数学