Ramification theory of automorphic representations and arithmetic of special L-values

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04784
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Okayama University
• Principal Investigator: Yoshi-Hiro Ishikawa 岡山大学, 自然科学研究科, 助教 (50294400)
• Co-Investigator(Kenkyū-buntansha): 都築 正男 上智大学, 理工学部, 教授 (80296946) ; 安田 正大 大阪大学, 理学研究科, 准教授 (90346065) ; 高野 啓児 香川大学, 教育学部, 准教授 (40332043)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 保型形式 / 表現論 / H-周期 / L-関数

Outline of Final Research Achievements

Number theory investigation usually involves quite vast area of deep　mathematics,like as the Fermat Last Theolem does. The Langlands Program, which led to the settlement of FLT, has been the central strategy of arithmetic since 70s. We follow the LP to study the ramification theory of the group U(3) representations in view point of L‐/ε‐factors. Our approach is resorting to integral presentations of L‐function of automorphic forms, whose ramified factors give us arithmetic info. The point is to find nice Whittaker functions appearing in the ramified factor. We can successfully detect where/which the nice ones are only in the case of Real/unramified U(3).

Free Research Field

整数論