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Local densities of quadratic forms and related problems

Research Project

Project/Area Number 06640003
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionMuroran Institute of Technology

Principal Investigator

KATSURADA Hidenori  Muroran Institute of Technology, 工学部, 教授 (80133792)

Co-Investigator(Kenkyū-buntansha) TAKEGAHARA Yugen  Muroran Institute of Technology, 工学部, 助教授 (10211351)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1995: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1994: ¥1,100,000 (Direct Cost: ¥1,100,000)
KeywordsLocal densities / Siegel-Eisenstein series / Maass zeta function / ジーゲル アイゼンシュタイン級数 / マ-ス ゼータ関数 / ジーゲル-アイゼンシュタイン級数
Research Abstract

In this research, we found a recursion formula for local densitires, which is useful to give an explicit formula for local desities. Further applying this to Sigel-Eisenstein series, we gave several important results about the Fourier coefficients of Siegel-Eisenstein series.
First, we gave a precise information about the denominator of a power series of one variables defined by Y.Kitaoka.
Secondly, we gave an explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3.
Thirdly, we gave an explicit formula for Koecher-Maass Dirichlet series associated with Siegel-Eisenstein series. This is a joint work with T.Ibukiyama.
Finally we gave a precise information about the denominaotor and numerator of a power series of several variables attached to local densities of quadratic forms.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] Katsurada, H: "A certain formal power series of several variables attached to lacal densities of quadratic forms I" J. Number Theory.51. 169-209 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsurada, H: "A certain formal power series of several variables attached to lacal densities of quadratic forms II" Proc. Japan Acad.70. 208-211 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsurada, H: "On power series attache to local denisities" Proc. Japan Acad.71. 187-188 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsurada, H: "An explicit formula for the Fourier coeffcients of Siegel-Eisenstein series of degree 3" HokkaidoUniversitiy technical report series in mathematics. 38. 97-99 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsurada, H: "Calculation of the Fourier coefficients of Siegel Eisensetein series" 代数と計算機"シンポジウム報告集. (発表予定). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊吹山 知義(阪大) 桂田 英典: "A simple formula for Koecher-Maass Dirichlet series attached to Siegel-Eisenstein series," 数理研講究録"代数群と保型形式"シンポジウム報告集. (発表予定). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Katsurada: "A certain formal power series of several variables attached to local densities of quadratic forms I" J.Number Theory. 51. 169-209 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Katsurada: "A certain formal power series of several variables attached to local densities of quadratic forms II" Proc.Japan Acad.70. 208-211 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Katsurada: "On power series attached to local densities" Proc.Japan Acad.71. 187-188 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Katsurada: "An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3" Hokkaido Univ.tech.rep.ser.in math.38. 97-99 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Katsurada: "Calculation of the Fourier coefficients of Eisenstein series of degree 3" Proc.of the research conference on "Algebra and Computers". (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Ibukiyama and H.Katsurada: "A simple formula for Koecher-Maass Dirichlet series attached to Siegel-Eisenstein series" RIMS Koukyuroku. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuroda,H: "A certain formal power series of several variables attached to local densities of quadratic forms I" J.Number Theory. 51. 169-209 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Katsurada,H: "On power series attached to local densities" Proc.Japan Acad.71. 187-188 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Katsurada,H: "An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3" Hokkaido Universitiy technical report series in mathematics. 38. 97-99 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Katsurada,H: "Calculation of the Fourier coefficients of Siegel Eisenstein series" “代数と計算機"シンポジウム報告集. (発表予定). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 伊吹山知義: "A simple formula for Koecher-Maass Dirichlet series attached to siegel-Eisenstein series," 数理研講究録“代数群と保型形式"シンポジウム報告集. (発表予定). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Katsurada,H: "A certain formal power series of several variables attached to local densities of qundratic forms I" Jormal of Number Theory. 51(in press). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] Katsurada,H: "A cerfain formal power series sevpral variables attached to local densities of quadratic forms II" Proceedings of the Japan Academy. 70. 208-211 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Katsurada,H: "A recursion formula for local demsities" I.C.M-1994.Shor Communication ahstracts. 35- (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 桂田英典: "A recursion formula for local demsities" 日本数学会代数分科会講演アプストラクト. 13-14 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 桂田英典: "A certain formal power sevies attached to local densitiesIII" 日本数学会代数分科会講演アプストラクト. 15

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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