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Multiple zeta functions associated with root systems and their applications

Research Project

Project/Area Number 19740009
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

YASUSHI Komori  Nagoya University, 多元数理科学研究科, 助教 (80343200)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,880,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥480,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
Keywords多重ゼータ / ルート系 / ワイル群 / 特殊値 / 母関数 / 関数等式 / コンパクトリー群 / qゼータ / シャッフル積 / 関数関係式 / 積分表示
Research Abstract

In the quantum gauge theory, which is one of those describing nature, the partition functions are considered to be the most fundamental and important quantities. Witten found that certain limits of the partition functions are described in terms of the volumes of certain spaces. These can be regarded as special values of zeta functions. In this study, we derived general formulas which give these special values, and furthermore presented some solutions to related problems.

Report

(5 results)
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (45 results)

All 2009 2008 2007 Other

All Journal Article (11 results) (of which Peer Reviewed: 4 results) Presentation (34 results)

  • [Journal Article] Kernel functions for difference operators of Ruijsenaars type and their applications2009

    • Author(s)
      Y.Komori, M.Noumi, J.Shiraishi
    • Journal Title

      SIGMA 5

    • Related Report
      2009 Final Research Report
  • [Journal Article] Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications2009

    • Author(s)
      Y.Komori, M.Noumi, J.Shiraishi
    • Journal Title

      Symmetry, Integrability and Geometry : Methods and Applications 5(054)

      Pages: 1-40

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Certain double series of Euler type and of Eisenstein type and Hurwitz numbers2009

    • Author(s)
      Y.Komori, K.Matsumoto, H.Tsumura
    • Journal Title

      RIMS kokyuroku 1639

      Pages: 104-122

    • Related Report
      2009 Annual Research Report
  • [Journal Article] On multiple Bernoulli polynomials and multiple L-functions of root systems2009

    • Author(s)
      Y.Komori, K.Matsumoto, H.Tsumura
    • Journal Title

      RIMS kokyuroku 1665

      Pages: 114-126

    • Related Report
      2009 Annual Research Report
  • [Journal Article] An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers2008

    • Author(s)
      Y.Komori
    • Journal Title

      Ramanujan J. 17,no.2

      Pages: 163-183

    • Related Report
      2009 Final Research Report
  • [Journal Article] Zeta and L-functions and Bernoulli polynomials of root systems2008

    • Author(s)
      Y.Komori, K.Matsumoto, H.Tsumura
    • Journal Title

      Proc.Japan Acad.Ser.A Math.Sci. 84,no.5

      Pages: 57-62

    • NAID

      120002232144

    • Related Report
      2009 Final Research Report
  • [Journal Article] Zeta and L-functions and Bernoulli polynomials of root systems2008

    • Author(s)
      Y. Komori, K. Matsumoto, H. Tsumura
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci. 84

      Pages: 57-62

    • NAID

      120002232144

    • Related Report
      2009 Self-evaluation Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An integral representation of the Mordell- Tornheim double zeta function and its values at non-positive integers2008

    • Author(s)
      Y. Komori
    • Journal Title

      Ramanujan J. 17

      Pages: 163-182

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers2008

    • Author(s)
      Y. Komori
    • Journal Title

      Ramanujan J. 17

      Pages: 163-182

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zeta-functions of root systems, in The conference on L-Functions2007

    • Author(s)
      Y.Komori, K.Matsumoto, H.Tsumura
    • Journal Title

      World Scientific(edited by L.Weng, M.Kaneko)

    • Related Report
      2009 Final Research Report
  • [Journal Article] An introduction to the theory of zeta-functions of root systems

    • Author(s)
      Y.Komori, K.Matsumoto, H.Tsumura
    • Journal Title

      MSJ Memoirs Vol.21

      Pages: 115-140

    • Related Report
      2009 Final Research Report
  • [Presentation] (G,P)に付随するWengゼータ関数の関数等式について2009

    • Author(s)
      小森靖
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      東京大学
    • Year and Date
      2009-12-09
    • Related Report
      2009 Final Research Report
  • [Presentation] (G, P)に付随するWengゼータ関数の関数等式について2009

    • Author(s)
      小森靖
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      東京大学
    • Year and Date
      2009-12-09
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] (G,P)に付随するWengゼータ関数の関数等式について.2009

    • Author(s)
      小森靖
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      東京大学
    • Year and Date
      2009-12-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems2009

    • Author(s)
      Y. Komori
    • Organizer
      l'atelier Zeta III
    • Place of Presentation
      Univ.Jean-Monnet, France
    • Year and Date
      2009-11-23
    • Related Report
      2009 Final Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems2009

    • Author(s)
      Y. Komori
    • Organizer
      l'atelier Zeta III
    • Place of Presentation
      Univ. Jean-Monnet, France.
    • Year and Date
      2009-11-23
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems.2009

    • Author(s)
      Y.Komori
    • Organizer
      I'atelier Zeta III
    • Place of Presentation
      Univ.Jean-Monnet, France
    • Year and Date
      2009-11-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] ルート系の多重ベルヌーイ多項式と多重L関数について2009

    • Author(s)
      小森靖
    • Organizer
      数学談話会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2009-09-10
    • Related Report
      2009 Final Research Report
  • [Presentation] ルート系の多重ベルヌーイ多項式と多重L関数について.2009

    • Author(s)
      小森靖
    • Organizer
      数学談話会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2009-09-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] ルート系の多重ベルヌーイ多項式と多重L関数について2009

    • Author(s)
      小森靖
    • Organizer
      表現論と組合せ論
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-08-27
    • Related Report
      2009 Final Research Report
  • [Presentation] ルート系の多重ベルヌーイ多項式と多重L関数について.2009

    • Author(s)
      小森靖
    • Organizer
      表現論と組合せ論
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-08-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] Functional equations for Weng's zeta functions for (G,P)2009

    • Author(s)
      小森靖
    • Organizer
      代数学セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2009-06-19
    • Related Report
      2009 Final Research Report
  • [Presentation] Functional equations for Weng's zeta functions for (G,P).2009

    • Author(s)
      Y.Komori
    • Organizer
      代数学セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2009-06-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Functional equations for Weng's zeta functions for (G,P)2009

    • Author(s)
      小森靖
    • Organizer
      解析数論セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2009-06-17
    • Related Report
      2009 Final Research Report
  • [Presentation] Functional equations for Weng's zeta functions for (G,P).2009

    • Author(s)
      小森靖
    • Organizer
      解析数論セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2009-06-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems2009

    • Author(s)
      小森靖, 松本耕二, 津村博文
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-27
    • Related Report
      2009 Final Research Report
  • [Presentation] Hurwitz-Lerch多重ゼータ関数の面積分表示と多重ベルヌーイ数2009

    • Author(s)
      小森靖
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-27
    • Related Report
      2009 Final Research Report
  • [Presentation] 多重ゼータ関数の面積分表示と多重ベルヌーイ数2009

    • Author(s)
      小森靖
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems2008

    • Author(s)
      Y. Komori
    • Organizer
      Oberseminar ZAHLENTHEORIE
    • Place of Presentation
      Wurzburg Univ., Germany
    • Year and Date
      2008-11-27
    • Related Report
      2009 Final Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems2008

    • Author(s)
      Y. Komori
    • Organizer
      Oberseminar ZAHLENTHEORIE
    • Place of Presentation
      Wuerzburg University, Gemiany
    • Year and Date
      2008-11-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] Certain double series of Euler type and of Eisenstein type and Hurwitz numbers (II)2008

    • Author(s)
      Y. Komori, K.Matsumoto, H.Tsumura
    • Organizer
      New Aspects of Analytic Number Theory
    • Place of Presentation
      京都大学
    • Year and Date
      2008-10-29
    • Related Report
      2009 Final Research Report
  • [Presentation] Certain double series of Euler type and of Eisenstein type and Hurwitz numbers (I)2008

    • Author(s)
      Y. Komori, K.Matsumoto, H.Tsumura
    • Organizer
      New Aspects of Analytic Number Theory
    • Place of Presentation
      京都大学
    • Year and Date
      2008-10-28
    • Related Report
      2009 Final Research Report
  • [Presentation] Certain double series of Euler type and of Eisenstein type and Hurwitz numbers (I)2008

    • Author(s)
      小森靖
    • Organizer
      New Aspects of Analytic Number Theory
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-10-28
    • Related Report
      2008 Annual Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple zeta functions of root systems2008

    • Author(s)
      Y. Komori
    • Organizer
      Elliptic integrable systems, isomonodromy problems, and hypergeometric functions
    • Place of Presentation
      Max Planck Institute for Mathematics, Germany.
    • Year and Date
      2008-07-21
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Multiple Bernoulli polynomials and multiple zeta functions of root systems2008

    • Author(s)
      Y. Komori
    • Organizer
      Elliptic integrable systems, isomonodromy problems, and hynergeometric functions
    • Place of Presentation
      Max Planck Institute for Mathematics, Germany
    • Year and Date
      2008-07-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] 多重ゼータ関数の積分表示と多重ベルヌーイ数2008

    • Author(s)
      小森靖
    • Organizer
      整数論セミナー
    • Place of Presentation
      津田塾大学
    • Year and Date
      2008-06-12
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems2008

    • Author(s)
      Y. Komori, K.Matsumoto, H.Tsumura
    • Organizer
      French-Japanese Winter School on Zeta and L-functions
    • Place of Presentation
      マホロバマインズ三浦海岸
    • Year and Date
      2008-01-09
    • Related Report
      2009 Final Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems.2008

    • Author(s)
      小森 靖
    • Organizer
      French-Japanese Winter School on Zeta and L-functions
    • Place of Presentation
      マホロバマインズ三浦海岸
    • Year and Date
      2008-01-09
    • Related Report
      2007 Annual Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple zeta functions of root systems2008

    • Author(s)
      Y. Komori
    • Organizer
      Elliptic integrable systems, isomonodromy problems, and hypergeometric functions
    • Place of Presentation
      Max Planck Institute for Mathematics, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] 重ゼータ関数の積分表示について2007

    • Author(s)
      小森靖
    • Organizer
      解析数論セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-12-19
    • Related Report
      2009 Final Research Report
  • [Presentation] An integral representation of multiple zeta-functions2007

    • Author(s)
      Y. Komori
    • Organizer
      Journees autour des series de Dirichlet
    • Place of Presentation
      Univ.Lille 1, France
    • Year and Date
      2007-11-13
    • Related Report
      2009 Final Research Report
  • [Presentation] An integral representation of multiple zeta-functions.2007

    • Author(s)
      Y. Komori
    • Organizer
      Journees autour des series de Dirichlet
    • Place of Presentation
      Lille 1 University, France.
    • Year and Date
      2007-11-13
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] An integral representation of multiple zeta-functions.2007

    • Author(s)
      小森 靖
    • Organizer
      Journees autour des series de Dirichlet
    • Place of Presentation
      Lille 1 University, France
    • Year and Date
      2007-11-13
    • Related Report
      2007 Annual Research Report
  • [Presentation] n multiple Bernoulli polynomials and multiple L-functions of root systems2007

    • Author(s)
      Y. Komori, K.Matsumoto, H.Tsumura
    • Organizer
      Analytic Number Theory and Related Areas
    • Place of Presentation
      京都大学
    • Year and Date
      2007-10-19
    • Related Report
      2009 Final Research Report
  • [Presentation] On multiple Bernoulli polynomials and multiple L-functions of root syst ems.2007

    • Author(s)
      小森 靖
    • Organizer
      Analytic Number Theory and Related Areas
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-10-19
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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