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Arithmetic study of modular forms belonging to the Maass space

Research Project

Project/Area Number 21840036
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionThe University of Tokushima

Principal Investigator

YOSHINORI Mizuno  The University of Tokushima, 大学院・ソシオテクノサイエンス研究部, 准教授 (30546388)

Project Period (FY) 2009 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥1,911,000 (Direct Cost: ¥1,470,000、Indirect Cost: ¥441,000)
Fiscal Year 2010: ¥884,000 (Direct Cost: ¥680,000、Indirect Cost: ¥204,000)
Fiscal Year 2009: ¥1,027,000 (Direct Cost: ¥790,000、Indirect Cost: ¥237,000)
Keywordsアイゼンシュタイン級数 / ケッヒャー・マース級数 / カトック・サルナック対応 / フーリエ係数 / 類数 / マース空間 / モジュラー形式 / ジーゲル・アイゼンシュタイン級数 / マース形式 / テータリフト / 二次形式 / 明示公式 / 合同
Research Abstract

We determined a proportional constant which appeares in three dimensional analogue of the Katok-Sarnak type formula.
We studied p-adic Hermitian-Eisenstein series of low weight by using Hecke's convergent factor.
We expressed average values of Eisenstein series over CM points on n-dimensional hyperbolic space in terms of a Dirichlet series whose coefficients are the number of the solutions of quadratic congruences.
We gave a good definition of Koecher-Maass series for indefinite Fourier coefficients of real analytic Siegel-Eisenstein series of degree 2 and weight 2. We then proved a meromorphic continuation and a functional equation of the Koecher-Maass series.

Report

(3 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • Research Products

    (13 results)

All 2011 2010 2009 Other

All Journal Article (8 results) (of which Peer Reviewed: 5 results) Presentation (2 results) Remarks (3 results)

  • [Journal Article] Some congruences for Saito-Kurokawa lifts2010

    • Author(s)
      Yoshinori Mizuno Shoyu Nagaoka
    • Journal Title

      Abhandlungen aus dem Mathematischen Semiinar der Universitat Hamburg 80巻

      Pages: 9-23

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectral theory on 3-dimensional hyperbolic space and Hermitian modular forms (a joint work with R. Matthes)2010

    • Author(s)
      Yoshinori Mizuno
    • Journal Title

      第4回福岡数論研究集会報告集 41巻

      Pages: 23-33

    • Related Report
      2010 Final Research Report
  • [Journal Article] Some congruences for Saito-Kurokawa lifts2010

    • Author(s)
      Yoshinori Mizuno, Shoyu Nagaoka
    • Journal Title

      Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

      Volume: 80巻 Pages: 9-23

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral theory on 3-dimensional hyperbolic space and Hermitian modular forms (a joint work with R.Matthes)2010

    • Author(s)
      Yoshinori Mizuno
    • Journal Title

      第4回福岡数論研究集会報告集

      Pages: 23-33

    • Related Report
      2009 Annual Research Report
  • [Journal Article] An explicit formula for the twisted Koecher-Maass series of the Saito-Kurokawa lift and their applications2009

    • Author(s)
      Hidenori Katsurada, Yoshinori Mizuno
    • Journal Title

      京都大学数理解析研究所講究録 No.1659

      Pages: 47-58

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Journal Article] Koecher-Maass series for positive definite Fourier coefficients of real analytic Siegel-Eisenstein series of degree 2, Bulletin of the London Math.2009

    • Author(s)
      Yoshinori Mizuno
    • Journal Title

      Soc 41巻

      Pages: 1017-1028

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] An explicit arithmetic formula for the Fourier coefficients of Siegel-Eisenstein series of degree two and square-free odd levels2009

    • Author(s)
      Yoshinori Mizuno
    • Journal Title

      Mathematische Zeitschrift 263巻

      Pages: 837-860

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Koecher-Maass series for positive definite Fourier coefficients of real analytic Siegel-Eisenstein series of degree 22009

    • Author(s)
      Yoshinori Mizuno
    • Journal Title

      Bulletin of the London Math. Soc. 41巻

      Pages: 1017-1028

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Dirichlet series associated with square of the class numbers2011

    • Author(s)
      水野義紀
    • Organizer
      京都大学数理解析研究所研究集会「保型形式と関連する跡公式,ゼータ関数の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-01-20
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 3次元上半空間のスペクトル理論とエルミート保型形式2009

    • Author(s)
      水野義紀
    • Organizer
      第4回福岡数論研究集会
    • Place of Presentation
      九州大学
    • Year and Date
      2009-08-25
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://pub2.db.tokushima-u.ac.jp/ERD/person/186508/profile-ja.html

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://pub2.db.tokushima-u.ac.jp/ERD/person/186508/profile-ja.html

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://pub2.db.tokushima-u.ac.jp/ERD/person/186508/profile-ja.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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