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Hilbert type automorphic forms and its application

Research Project

Project/Area Number 06640084
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHOSEI University

Principal Investigator

HIRAMATSU Toyokazu  Engineering, Professor, 工学部, 教授 (40029674)

Co-Investigator(Kenkyū-buntansha) FUSE Mitsuo  Engineering, Lecturer, 工学部, 講師 (00120832)
TANAKA Hisao  Engineering, Professor, 工学部, 教授 (70061025)
ANDO Shiro  Engineering, Professor, 工学部, 教授 (60061016)
NAGASAKA Kenji  Engineering, Professor, 工学部, 教授 (40000187)
Project Period (FY) 1994 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1996: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1994: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsAutomorphic forms / Algebraic geometric code / rational point / Kloosterman sum / uniform distribution / Sato-Tate conjecture / Fractal dimension / computational complexity / 有限体 / kloasterman和 / Sato-Tate予想 / 多変数保型形式 / ヘッケ作用素 / セルバーグ型等 / 線形符号 / ヒルベルト型保型形式 / セルバーグ型ゼータ関数 / フラクタル
Research Abstract

Let C be the basic Kloosterman code over any finite field. We proved that the weights of the code C are uniformly distributed with respect to Sato-Tate measure. Further more, by generalizing this result we gave a new code C_n, to be called the hyperkloosterman code (C=C_2), and deduced a uniform distribution theorem for the weights of the codewords of C_n.
In 1981, D.Goppa found a surprising link between coding theory and algebraic geometry. Namely he used rational points on algebraic curves to construct code over a finite field. We gave a short survey of the work done on algebraic geometric codes, automorphic forms and number theory during the last 15 years.

Report

(4 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • 1994 Annual Research Report
  • Research Products

    (36 results)

All Other

All Publications (36 results)

  • [Publications] H.Tanaka: "Determining the levels of some special complexity classes of sets in the Kleene arithmetical hierarchy" Tokyo J.of Math.17. 125-133 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Hiramatsu: "Uniform distribution of the weight of the Kloasterman codes" SUT J.of Math.31. 29-32 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 長坂建二: "フラクタル次元とその変化の推定" 法政大学計算センター研究報告. 8. 109-114 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Ando: "Multiple colar version of the star of David thearem on Pascal's triangle and related arrays of numbers" Applications of Fibonacci Numbers. 6. 31-45 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Tanaka: "On relativized probabilistic polynomial time algorithms" J.Math.Soc.Japan. 49. 15-29 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 平松豊一: "有限体上の代数曲線の有理点と線形符号" 法政大学計算センター研究報告. 10. (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 長坂建二: "新版解析学" 放送大学教育振興会, 243 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 平松豊一: "応用代数学" 裳華房(予定), (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Tanaka: "Determining the levels of some special complexity classes of sets in the Kleene arithmetical hierarchy" Tokyo J.of Math. Vol.17. 125-133 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Hiramatsu: "Uniform distribution of the weight of the Kloosterman codes" SUT J.of Math.Vol.31. 29-32 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Nagasaka: "Estimation method for the fractal dimension and its turning point of planar curves" Bulletin of Computer Center, Hosei University. Vol.8. 109-114 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Ando: "Multiple color version of the star of David theorem on Pascal's triangle and related arrays of numbers" Applications of Fibonacci Numbers. Vol.6. 31-45 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Tanaka: "On relativized probabilistic polynomial time algorithms" J.of Math. Soc. Japan. Vol.49. 15-29 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Hiramatsu: "Rational points on algebraic curves over finite fields and linear codes" Bulletin of Computer Center, Hosei University. Vol.10. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 平松豊一: "Unifarm distribution of the weight of the hyperkloasterman codes" 津田塾大学数学・計算科学研・研究所報. 12. 60-68 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 平松豊一: "有限体上の代数曲線の有理点と線形符号" 法政大学計算センター研究報告. 10. 10- (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 安藤四郎: "Minimal center covering stars with respect to LCM in Pascal's pyramid and ito generalizations" Applications of Fibonacci Numbers. 6. 23-30 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 安藤四郎: "Counting number of equivalance classes of (m,F) sequences and their generalizations" The Fibonacci Quarterly. 35・1. 3-8 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 田中尚夫: "数学基礎論的手法の計算量理論への応用" 数学(日本数学会). 48・4. 372-384 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 田中 尚夫: "On relativized probabilistic polynomial time algarithms" J.Math.Soc.Japan. 49・1. 15-30 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 平松豊一: "応用代数学" 裳華房(予定), (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 長坂建二: "新版統計学" 放送大学教育振興会, (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 平松豊一: "Some results of the Zetterberg codes" 法政大学工学部研究集報. 31. 19-26 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 平松豊一: "Uniform distribution of the weights of the Kloosterman codes" SUT J. of Math. 31. 29-32 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 知念宏司(第一著者): "Uniform distribution of the weights of the Hyperkloosterman code" 津田塾大学数学計算機;科学研究所報. 12. 60-68 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 目次康男(第一著者): "2次整数上の符号構成" 情報理論とその応用シンポジウム予稿集. 18. 753-756 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 安藤四郎: "On the minimal center covering stors with respect to GCD in Pascal′s pyramid and its generalizations" Applications of Fibonacci Numbers. 5. 37-43 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 田中尚夫: "確率的多項式時間計算量クラスBPPの内部の時間階層について" 法政大学工学部研究集報. 31. 7-11 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 平松 豊一: "Goppa codes and number theory" 整数論シンポジウム報告書. 150-166 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] T Hiramatsu.T Ochiai.: "Some results of the Zetterberg codes" 法政大学工学部研究集報. 31. 19-26 (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] T Hiramatsu.: "Uniform distribution of the weights of the Kloosterman codes" SUT J.of Math.31(to appear). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] K Nagasaka.: "Remarks on asymptotic behaviour of linear recurrence sequences" Applications of Fibonacci Numbers. 6(to appear). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 長坂 健二,高橋 朋一: "フラクタル次元とその変化の推定" 法政大学計算センター研究報告. 8(to appear). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] H Tanaka.: "Determining the levels of some special complexity classes of sets inthe Kleene arithmetical hierarchy" Tokyo J.of Math.17. 125-133 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] S Ando.: "On a system of sequences defined by a recurrence relation" Fibonacci Quarterly. (to appear).

    • Related Report
      1994 Annual Research Report
  • [Publications] 布施 光男: "江戸時代電気技術はどう培われたか" 電学誌. 115. 35-39 (1995)

    • Related Report
      1994 Annual Research Report

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

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