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Research on density theorems and invariants with zeta functions and trace formulas

Research Project

Project/Area Number 20740027
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionInstitute of Systems & Information Technologies KYUSHU

Principal Investigator

HASHIMOTO Yasufumi  Institute of Systems & Information Technologies KYUSHU, 情報セキュリティ研究室, 研究員 (30452733)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsゼータ関数 / 跡公式 / 素測地線定理 / length spectrum / ラプラシアン / Length spectrum / セルバーグ跡公式 / セルバーグゼータ関数 / 素元定理 / リーマン面 / 合同部分群 / 不定値二元二次形式
Research Abstract

There are deep connections between zeta functions and density theorems, such like Riemann's zeta functions and the prime number theorem, Selberg's zeta functions and the prime geodesic theorem. In this research, we aim to explain the properties of manifolds by studying density theorems and invariants with zeta functions and trace formulas. Especially, the length spectrum defined by the set of length of closed geodesics on a hyperbolic manifold is important to characterize the manifold. The main results on this research is to describe the length spectra for arithmetic surfaces in terms of objects in the classical number theory, and to obtain an asymptotic formula to explain ``average" of the behavior of the multiplicity of the length spectrum. As an application, we also get one kind of improvements of the asymptotic formula for the class numbers of indefinite binary quadratic forms.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (45 results)

All 2011 2010 2009 2008 Other

All Journal Article (16 results) (of which Peer Reviewed: 8 results) Presentation (29 results)

  • [Journal Article] Algorithms to solve massively under-defined systems of multivariate quadratic equations2011

    • Author(s)
      Y.Hashimoto
    • Journal Title

      IEICE Trans.Fundamentals

      Volume: E94-A(未定)

    • NAID

      10029802211

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algorithms to solve massively under-defined systems of multivariate quadratic equations2010

    • Author(s)
      Y.Hashimoto
    • Journal Title

      Proceedings (Industrial Track) of the 8th International Conference on Applied Cryptography and Network Security

      Pages: 26-37

    • NAID

      10029802211

    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Journal Article] On small secret key attack against RSA with high bits known prime factors2010

    • Author(s)
      Y.Hashimoto
    • Journal Title

      Proceedings (short papers) of 5th International Workshop on Security

      Pages: 14-25

    • Related Report
      2010 Final Research Report
  • [Journal Article] Partial zeta functions2010

    • Author(s)
      Y.Hashimoto
    • Journal Title

      Archiv der Mathematik 95

      Pages: 363-372

    • Related Report
      2010 Final Research Report
  • [Journal Article] Partial zeta functions2010

    • Author(s)
      Y.Hashimoto
    • Journal Title

      Archiv der Mathematik

      Volume: 95 Pages: 363-372

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On small secret key attack against RSA with high bits known prime factors2010

    • Author(s)
      Y.Hashimoto
    • Journal Title

      Proceedings (short papers) of 5th International Workshop on Security (IWSEC2010)

      Pages: 14-25

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 合同部分群に関するlength spectrumの重複度について2010

    • Author(s)
      橋本康史
    • Journal Title

      2010年度表現論シンポジウム講演集

      Pages: 66-81

    • NAID

      130008004926

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Prime and zero distributions for meromorphic Euler products2009

    • Author(s)
      Y.Hashimoto
    • Journal Title

      5th Asian Mathematical Conference Proceedings 1

      Pages: 255-261

    • Related Report
      2010 Final Research Report
  • [Journal Article] On asymptotic behavior of composite integers n=pq2009

    • Author(s)
      Y.Hashimoto
    • Journal Title

      J.Math-for- Industry 1

      Pages: 45-49

    • NAID

      120001177117

    • Related Report
      2010 Final Research Report
  • [Journal Article] Prime and zero distributions for meromorphic Euler products2009

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      5th Asian Mathematical Conference Proceedings 1

      Pages: 255-261

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On asymptotic behavior of composite integers n=qp2009

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      J. Math-for-Industry 1

      Pages: 45-49

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytic properties of partial zeta functions2008

    • Author(s)
      Y.Hashimoto
    • Journal Title

      RIMS Kokyuroku Bessatsu B-7

      Pages: 73-82

    • Related Report
      2010 Final Research Report
  • [Journal Article] Distributions of multiplicities in length spectra for hyperbolic Riemann surfaces2008

    • Author(s)
      Y.Hashimoto
    • Journal Title

      OCAMI Studies 2-2

      Pages: 195-199

    • Related Report
      2010 Final Research Report
  • [Journal Article] 部分ゼータ関数の解析性2008

    • Author(s)
      橋本康史
    • Journal Title

      数理解析研究所講究録別冊 B-7

      Pages: 73-82

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Distributions of multiplicities in length spectra for hyperbolic Riemann surfaces2008

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      Complex Analysis and its Applications, OCAMI Studies 2

      Pages: 195-199

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Distributions of length multiplicities for Riemann surfaces

    • Author(s)
      Y.Hashimoto
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: (未定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 多変数暗号に関する故障利用攻撃について2011

    • Author(s)
      橋本康史・高木剛
    • Organizer
      2011年度暗号と情報セキュリティシンポジウム
    • Place of Presentation
      福岡県北九州市
    • Year and Date
      2011-01-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] 多変数暗号に関する故障利用攻撃について2011

    • Author(s)
      橋本康史, 高木剛
    • Organizer
      2011年度暗号と情報セキュリティシンポジウム
    • Place of Presentation
      リーガロイヤルホテル小倉(福岡県北九州市)
    • Related Report
      2010 Final Research Report
  • [Presentation] 合同部分群に関するlength spectrumの重複度について2011

    • Author(s)
      橋本康史
    • Organizer
      2011年度日本数学会年会函数論分科会
    • Place of Presentation
      早稲田大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] On small secret key attack against RSA with high bits known prime factors2010

    • Author(s)
      Y.Hashimoto
    • Organizer
      5th International Workshop on Security (IWSEC2010)
    • Place of Presentation
      兵庫県神戸市
    • Year and Date
      2010-11-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] 合同部分群に関するlength spectrumの重複度について2010

    • Author(s)
      橋本康史
    • Organizer
      2010年度表現論シンポジウム
    • Place of Presentation
      静岡県伊豆の国市
    • Year and Date
      2010-11-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] On multiplicities in length spectra for congruence subgroups2010

    • Author(s)
      橋本康史
    • Organizer
      Zetas and Limit Laws in OKINAWA 2010
    • Place of Presentation
      沖縄県宜野湾市
    • Year and Date
      2010-11-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Algorithms to solve massively under-defined systems of multivariate quadratic equations2010

    • Author(s)
      Y.Hashimoto
    • Organizer
      Industrial Track in 8th International Conference on Applied Cryptography and Network Security
    • Place of Presentation
      中国北京市
    • Year and Date
      2010-06-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] 不定値二元二次形式の類数和に関する漸近公式について2010

    • Author(s)
      橋本康史
    • Organizer
      2010年度日本数学会年会代数学分科会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 素因子の上位ビットが既知で秘密鍵が小さいRSAに対する攻撃法について2010

    • Author(s)
      橋本康史
    • Organizer
      2010年度暗号と情報セキュリティシンポジウム
    • Place of Presentation
      香川県高松市
    • Year and Date
      2010-01-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] 素因子の上位ビットが既知で秘密鍵が小さいRSA に対する攻撃法について2010

    • Author(s)
      橋本康史
    • Organizer
      2010年度暗号と情報セキュリティシンポジウム
    • Place of Presentation
      サンポートホール高松(香川県高松市)
    • Related Report
      2010 Final Research Report
  • [Presentation] 不定値二元二次形式の類数和に関する漸近公式について2010

    • Author(s)
      橋本康史
    • Organizer
      第15回代数学若手研究会
    • Place of Presentation
      名古屋大学
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 不定値二元二次形式の類数和に関する漸近公式について2010

    • Author(s)
      橋本康史
    • Organizer
      2010年度日本数学会年会代数学分科会
    • Place of Presentation
      慶応義塾大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Algorithms to solve massively under-defined systems of multivariate quadratic equations2010

    • Author(s)
      Y.Hashimoto
    • Organizer
      Industrial Track in 8th International Conference on Applied Cryptography and Network Security
    • Place of Presentation
      北京工大建国飯店(中国北京市)
    • Related Report
      2010 Final Research Report
  • [Presentation] 不定値二元二次形式の類数和に関する漸近公式2010

    • Author(s)
      橋本康史
    • Organizer
      第9回仙台広島整数論集会
    • Place of Presentation
      東北大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 不定値二元二次形式の類数和に関する漸近公式2010

    • Author(s)
      橋本康史
    • Organizer
      大阪大学整数論・保型形式セミナー
    • Place of Presentation
      大阪大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 不定値二元二次形式の類数和に関する漸近公式2010

    • Author(s)
      橋本康史
    • Organizer
      研究集会「表現論がつなぐ数論・解析学・組合せ論」
    • Place of Presentation
      愛媛大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 合同部分群に関するlengthspectrumの重複度について2010

    • Author(s)
      橋本康史
    • Organizer
      2010年度表現論シンポジウム
    • Place of Presentation
      おおとり荘(静岡県伊豆の国市)
    • Related Report
      2010 Final Research Report
  • [Presentation] On multiplicities in length spectra for congruence subgroups2010

    • Author(s)
      Y.Hashimoto
    • Organizer
      Zetas and Limit Laws in OKINAWA 2010
    • Place of Presentation
      沖縄コンベンションセンター(沖縄県宜野湾市)
    • Related Report
      2010 Final Research Report
  • [Presentation] On small secret key attack against RSA with high bits known prime factors2010

    • Author(s)
      Y.Hashimoto
    • Organizer
      5th International Workshop on Security (IWSEC2010)
    • Place of Presentation
      神戸国際会議場(兵庫県神戸市)
    • Related Report
      2010 Final Research Report
  • [Presentation] Asymptotic formulas of class number sums in arithmetic progressions for indefinite binary quadratic forms2009

    • Author(s)
      Yasufumi Hashimoto
    • Organizer
      Zetas and Limit Laws in OH-NAWA 2009
    • Place of Presentation
      沖縄県宜野湾市
    • Year and Date
      2009-11-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] 不定値二元二次形式の類数の部分和に関する漸近公式について2009

    • Author(s)
      橋本康史
    • Organizer
      2008年度日本数学会代数学分科会
    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2009-09-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] Prime and zero distributions for meromorphic Euler products2009

    • Author(s)
      Yasufumi Hashimoto
    • Organizer
      5th Asian Mathematical Conference
    • Place of Presentation
      マレーシア・クアラルンプール市
    • Year and Date
      2009-06-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] 変数の個数が方程式の個数よりも十分大きい多変数連立二次方程式の解法について2009

    • Author(s)
      橋本康史
    • Organizer
      2009年度暗号と情報セキュリティシンポジウム
    • Place of Presentation
      大津プリンスホテル(滋賀県大津市)
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] 変数の個数が方程式の個数よりも十分大きい多変数連立二次方程式の解法について2009

    • Author(s)
      橋本康史
    • Organizer
      ワークショップ「安全な社会基盤への計算量的数論の応用-次世代暗号技術の最先端理論より-
    • Place of Presentation
      九州大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Prime and zero distributions for meromorphic Euler products2009

    • Author(s)
      Y.Hashimoto
    • Organizer
      5th Asian Mathematical Conference
    • Place of Presentation
      Putra World Trade Centre(マレーシア,クアラルンプール市)
    • Related Report
      2010 Final Research Report
  • [Presentation] オイラー積で表される有理型なゼータ関数の素元分布と零点分布について2009

    • Author(s)
      橋本康史
    • Organizer
      研究集会「表現論がつなぐ数学」
    • Place of Presentation
      ホテルロコアナハ(沖縄県那覇市)
    • Related Report
      2010 Final Research Report
  • [Presentation] Asymptotic formulas of class number sums in arithmetic progressions for indefinite binary quadratic forms2009

    • Author(s)
      Y.Hashimoto
    • Organizer
      Zetas and Limit Laws in OKINAWA 2009
    • Place of Presentation
      フェストーネ(沖縄県宜野湾市)
    • Related Report
      2010 Final Research Report
  • [Presentation] 不定値二元二次形式の類数の部分和に関する漸近公式について2008

    • Author(s)
      橋本康史
    • Organizer
      2008年度日本数学会年会代数学分科会
    • Place of Presentation
      東京工業大学
    • Related Report
      2010 Final Research Report
  • [Presentation] n=pq型の合成数の分布について2008

    • Author(s)
      橋本康史
    • Organizer
      Zetas and Limit Laws in OKINAWA 2008
    • Place of Presentation
      沖縄コンベンションセンター(沖縄県宜野湾市)
    • Related Report
      2010 Final Research Report 2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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