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On p-adic aspects of automorphic forms and their applications

Research Project

Project/Area Number 26800016
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionHiroshima University

Principal Investigator

Kawamura Hisa-aki  広島大学, 理学研究科, 助教 (00533746)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords保型形式 / p進保型形式 / L函数 / p進L函数 / 楕円曲線 / p進L関数 / 国際情報交換
Outline of Final Research Achievements

For certain automorphic forms on reductive algebraic groups and associated L-functions, in particular, the so-called Siegel Eisenstein series, Duke-Imamoglu-Ikeda lift and standard L-functions for the symplectic and unitary groups, the p-adic aspects of them have been studied from various viewpoints arising out of the theories of classical and p-adic automorphic forms. More precisely, by constructing p-adic analytic families of the above-mentioned automorphic forms and the Lambda-adic forms, we study the p-adic standard L-functions for the symplectic and unitary groups.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (3 results)

All 2017 2015 2014

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Open Access: 2 results) Presentation (1 results) (of which Invited: 1 results)

  • [Journal Article] Ikeda's conjecture on the period of the Duke-Imamoglu-Ikeda lift2015

    • Author(s)
      Hidenori Katsurada; Hisa-aki Kawamura
    • Journal Title

      Proceedings of the London Mathematical Society

      Volume: 印刷中

    • NAID

      120006459648

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Koecher-Maass series of a certain half-integral weight modular form related with the Duke-Imamoglu-Ikeda lift2014

    • Author(s)
      H. Katsurada and H. Kawamura
    • Journal Title

      Acta Arithmetica

      Volume: 162 Issue: 1 Pages: 1-42

    • DOI

      10.4064/aa162-1-1

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] The semi-ordinary p-stabilization of Siegel Eisenstein series for symplectic groups and unitary groups2017

    • Author(s)
      Hisa-aki Kawamura
    • Organizer
      Collaborative Number Theory Seminar at the CUNY Graduate Center
    • Place of Presentation
      City University of New York (United States of America)
    • Related Report
      2016 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2019-03-29  

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