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2018 Fiscal Year Final Research Report

Periods of automorphic forms and special values of L-functions

Research Project

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Project/Area Number 26287003
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

Ichino Atsushi  京都大学, 理学研究科, 准教授 (40347480)

Co-Investigator(Kenkyū-buntansha) 池田 保  京都大学, 理学研究科, 教授 (20211716)
Project Period (FY) 2014-04-01 – 2019-03-31
Keywords周期 / 保型表現 / テータ対応
Outline of Final Research Achievements

In this research, we have studied periods of automorphic forms on quaternion algebras. In particular, we aimed at an explicit realization of the functoriality called the Jacquet-Langlands correspondence in terms of absolute Hodge cycles.
Also, we have studied the automorphic discrete spectrum of metaplectic groups. In particular, we aimed at a generalization of the Arthur classification for classical groups and the theory of half-integral weight modular forms by Shimura and Waldspurger.

Free Research Field

数論

Academic Significance and Societal Importance of the Research Achievements

Jacquet-Langlands対応の絶対Hodgeサイクルによる具体的な実現に向けて、大きな成果を上げることができた。この成果は30年以上の間停滞していた分野に著しい進展をもたらす、学術的意義の高いものである。またメタプレクティック群の保型離散スペクトルについて、緩増加部分を精密に記述することに成功した。この成果は、重さ半整数保型形式の理論を一新するものである。

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Published: 2020-03-30  

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