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The construction of the modular forms and the study of its arithmetic properties

Research Project

Project/Area Number 23740029
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionChiba Institute of Technology

Principal Investigator

GUNJI Keiichi  千葉工業大学, 工学部, 助教 (00550659)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords整数論 / 多変数保型形式 / アイゼンシュタイン級数 / 保型形式 / 国際情報交換 / 国際研究者交流
Outline of Final Research Achievements

Recentry, for the study of the number theory, investing modular forms, that are functions satisfiyng the certain transformation formula, is the main topics. The analisys of the modular forms of several variables is difficult in general. However we can construct them by using the methods of lifting, from the modular forms of one variable. Such lifts are relatively easy to analysis, and have many interesting arithmetic properties. In this study, we extend the results of the lifting, which are already known.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (4 results)

All 2015 2014 Other

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (2 results)

  • [Journal Article] On the Siegel-Eisenstein series of degree two for low weights2015

    • Author(s)
      Keiichi Gunji
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 68

    • NAID

      130005094196

    • Related Report
      2014 Annual Research Report
  • [Journal Article] On the Siegel-Eisenstein series of degree two for low weights2014

    • Author(s)
      Keiichi Gunji
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 未定

    • NAID

      130005094196

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] On Ikeda's lift of level p2014

    • Author(s)
      軍司圭一
    • Organizer
      愛媛大学ミニ研究集会
    • Place of Presentation
      愛媛大学理学部2号館(愛媛県松山市)
    • Year and Date
      2014-08-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] 自明指標に付随する分岐Siegel級数の計算

    • Author(s)
      Keiichi Gunji
    • Organizer
      保型形式の整数論月例セミナー
    • Place of Presentation
      東京大学数理科学研究科(東京都)
    • Related Report
      2013 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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