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Study of Fourier-Jacobi type spherical functions for Siegel modular forms of degree two and its application

Research Project

Project/Area Number 24540022
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionEhime University

Principal Investigator

HIRANO Miki  愛媛大学, 理工学研究科, 教授 (80314946)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsフーリエ・ヤコビ型球関数 / フーリエ・ヤコビ展開 / 保型L-関数 / ジーゲル保型形式 / ホイッタカー関数 / ランキン・セルバーグ型ゼータ積分
Outline of Final Research Achievements

We reaped a satisfactory result in a preliminary and a similar study to the main theme. The principal results are explicit evaluations of the zeta integrals of GL(3,C)×GL(2,C) which is an application of our explicit formulas of the non-class 1 principal series Whittaker functions on GL(3,C). These are important for the explicit theory of automorphic forms and their L-functions.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (1 results)

All 2015

All Presentation (1 results)

  • [Presentation] Archimedean zeta integrals for GL(3)×GL(2)2015

    • Author(s)
      平野幹 石井卓 宮崎直
    • Organizer
      RIMS研究集会「モジュラー形式と保型表現」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-02-02 – 2015-02-06
    • Related Report
      2014 Annual Research Report

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Published: 2013-05-31   Modified: 2019-07-29  

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