Ramified components of automorphic representations: local theory and its application to special L-values

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540021
• 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: ISHIKAWA YOSHI-HIRO 岡山大学, 自然科学研究科, 助教 (50294400)
• Co-Investigator(Kenkyū-buntansha): TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946) ; YASUDA Seidai 大阪大学, 理学研究科, 准教授 (90346065) ; TAKANO Keiji 明石工業高等専門学校, 一般科目, 准教授 (40332043)
• Co-Investigator(Renkei-kenkyūsha): MIYAUCHI Michitaka 大阪府立大学, 高等教育推進機構, 教育拠点形成教員 (70533644)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 保型形式 / 表現論 / ε-因子 / H-周期

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 integralpresentations 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 in the case of　Real/unramified U(3). As an application to the global problem, we got algebraicity result for all the critical values of twisted L-function of generic cuspidal representaions on U(3).

Free Research Field

整数論