• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Studies on various multiple zeta-functions associated with root systems

Research Project

Project/Area Number 22540045
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KOMORI Yasushi  立教大学, 理学部, 准教授 (80343200)

Co-Investigator(Renkei-kenkyūsha) MATSUMOTO Kohji  名古屋大学, 大学院多元数理科学研究科, 教授 (60192754)
TSUMURA Hirofumi  首都大学東京, 大学院理工学研究科, 教授 (20310419)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords多重ゼータ関数 / 多重ゼータ / リー群 / ゲージ理論
Research Abstract

Both partition functions in quantum gauge theories and zeta-functions in mathematics, which play fundamental and important roles in each area, happen to coincide in some cases. Among them are the Witten zeta-functions. Special values of these zeta-functions at positive integers are the main objects and should be studied from various viewpoints. For this problem, we established a unified way to treat these values via their generating functions. We also obtained new functional relations and formulas for related zeta-functions and hypergeometric functions from the viewpoint of root systems.

Report

(4 results)
  • 2013 Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (38 results)

All 2012 2011 2010

All Journal Article (20 results) (of which Peer Reviewed: 20 results) Presentation (18 results) (of which Invited: 1 results)

  • [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebras III, in Multiple Dirichlet Series, L-functions and Automorphic Forms2012

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

      Progress in Mathematics

      Volume: Vol.300 Pages: 223-286

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebras III2012

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

      Progress in Math (Birkhauser)

      Volume: 300 Pages: 223-286

    • DOI

      10.1007/978-0-8176-8334-4_11

    • ISBN
      9780817683337, 9780817683344
    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Evaluation formulas of Cauchy-Mellin type for certain series involving hyperbolic functions2011

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

      Comment. Math. Univ. St. Pauli

      Volume: 60 Pages: 127-142

    • NAID

      110008739286

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Functional equations for double L-functions and values at non-positive integers2011

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

      Int. J. Number Theory

      Volume: 7 Pages: 1441-1461

    • NAID

      120005434484

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems2011

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

      RIMS Kokyuroku Bessatsu

      Volume: B28 Pages: 99-120

    • NAID

      120005438217

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems2011

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

      Math. Z

      Volume: 268 Pages: 993-1011

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple zeta values and zeta-functions of root systems2011

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

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

      Volume: 87, no.6 Pages: 103-107

    • NAID

      120005438215

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebras IV2011

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

      Glasg. Math. J

      Volume: 53 Pages: 185-206

    • NAID

      120005434485

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Evaluation formulas of Cauchy-Mellin type for certain series involving hyperbolic functions2011

    • Author(s)
      Yasushi Komori
    • Journal Title

      Comment.Math.Univ.St.Pauli

      Volume: 60 Pages: 127-142

    • NAID

      110008739286

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Functional equations for double L-functions and values at non-positive integers2011

    • Author(s)
      Yasushi Komori
    • Journal Title

      Int.J.Number Theory

      Volume: 7 Pages: 1441-1461

    • NAID

      120005434484

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems2011

    • Author(s)
      Yasushi Komori
    • Journal Title

      Math.Z

      Volume: 268 Pages: 993-1011

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Witten multiple zeta-functions associated with semisimple lie algebras IV2011

    • Author(s)
      Yasushi Komori
    • Journal Title

      Glasg.Math.J.

      Volume: 53 Pages: 185-206

    • NAID

      120005434485

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An integral representation of multiple Hurwitz-Lerch zeta functions and generalized multiple Bernoulli numbers2010

    • Author(s)
      Y. Komori
    • Journal Title

      Quart. J. Math.

      Volume: 61 Pages: 437-496

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Functional equations and functional relations for the Euler double zeta-function and its generalization of Eisenstein type2010

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

      Publ. Math. Debrecen

      Volume: 77 Pages: 15-31

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebras II2010

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

      J. Math. Soc. Japan

      Volume: 62, No.2 Pages: 355-394

    • NAID

      10026999060

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On multiple Bernoulli polynomials and multiple L-functions of root systems2010

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

      Proc. London Math. Soc.

      Volume: 100 Pages: 303-347

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] An integral representation of multiple Hurwitz-Lerch zeta functions and generalized multiple Bernoulli numbers2010

    • Author(s)
      Yasushi Komori
    • Journal Title

      Quart.J.Math.

      Volume: 61 Pages: 437-496

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On multiple Bernoulli polynomials and multiple L-functions of root systems2010

    • Author(s)
      Yasushi Komori
    • Journal Title

      Proc.London Math.Soc.

      Volume: 100 Pages: 303-347

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebra II2010

    • Author(s)
      Yasushi Komori
    • Journal Title

      J.Math.Soc.Japan

      Volume: 62 Pages: 355-394

    • NAID

      10026999060

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Functional equations and functional relations for certain double series of Euler type and of Eisenstein type2010

    • Author(s)
      Yasushi Komori
    • Journal Title

      Publ.Math.Debrecen

      Volume: 77 Pages: 15-31

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] ルート系に付随する多重ゼータ関数について2012

    • Author(s)
      小森靖
    • Organizer
      立教大学数理物理学研究センター第13回セミナー
    • Place of Presentation
      立教大学
    • Year and Date
      2012-12-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Zeta-functions of weight lattices of compact connected semisimple Lie groups2012

    • Author(s)
      Y. Komori
    • Organizer
      2012 Conference on L-functions
    • Place of Presentation
      Jeju, Korea
    • Year and Date
      2012-08-24
    • Related Report
      2013 Final Research Report
  • [Presentation] ルート系と多重ゼータ関数について2012

    • Author(s)
      小森靖
    • Organizer
      第5回多重ゼータおよびその周辺
    • Place of Presentation
      九州大学
    • Year and Date
      2012-01-27
    • Related Report
      2013 Final Research Report
  • [Presentation] ルート系と多重ゼータ関数について2012

    • Author(s)
      Yasushi Komori
    • Organizer
      第5回多重ゼータおよびその周辺
    • Place of Presentation
      九州大学(招待講演)
    • Year and Date
      2012-01-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] Wittenゼータ関数入門(II)2012

    • Author(s)
      小森靖
    • Organizer
      関西多重ゼータ研究会
    • Place of Presentation
      大阪工業大学
    • Year and Date
      2012-01-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Wittenゼータ関数入門(II)2012

    • Author(s)
      Yasushi Komori
    • Organizer
      関西多重ゼータ研究会
    • Place of Presentation
      大阪工業大学(招待講演)
    • Year and Date
      2012-01-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] ルート系に付随する多重ゼータ関数について2012

    • Author(s)
      小森 靖
    • Organizer
      数理物理学研究センター第13回セミナー
    • Place of Presentation
      立教大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Zeta-functions of weight lattices of compact connected semisimple Lie groups2012

    • Author(s)
      小森 靖
    • Organizer
      2012 Conference on L-functions
    • Place of Presentation
      韓国済州島
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] ルート系のゼータ関数とベルヌーイ関数(I)2011

    • Author(s)
      小森靖
    • Organizer
      明学セミナー
    • Place of Presentation
      明治学院大学
    • Year and Date
      2011-12-10
    • Related Report
      2013 Final Research Report
  • [Presentation] ルート系のゼータ関数とベルヌーイ関数(I)2011

    • Author(s)
      Yasushi Komori
    • Organizer
      明学セミナー
    • Place of Presentation
      明治学院大学(招待講演)
    • Year and Date
      2011-12-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] Euler Zagier zeta-functions and zeta-functions of root systems2011

    • Author(s)
      Y. Komori
    • Organizer
      Oberseminar zahlentheorie
    • Place of Presentation
      Wuerzburg, Germany
    • Year and Date
      2011-09-14
    • Related Report
      2013 Final Research Report
  • [Presentation] Euler-Zagier zeta-functions and zeta-functions of root systems2011

    • Author(s)
      Yasushi Komori
    • Organizer
      Oberseminar zahlentheorie
    • Place of Presentation
      Wuerzburg, Germany
    • Year and Date
      2011-09-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] Zeta-functions of root systems and of Lie groups2011

    • Author(s)
      Y. Komori
    • Organizer
      Analytic and probabilistic methods in number theory
    • Place of Presentation
      Palanga, Lithuania
    • Year and Date
      2011-09-07
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
  • [Presentation] リー群に付随するゼータ関数について2011

    • Author(s)
      小森靖
    • Organizer
      第4回ゼータ若手研究集会
    • Place of Presentation
      沖縄県青年会館
    • Year and Date
      2011-02-21
    • Related Report
      2013 Final Research Report 2010 Annual Research Report
  • [Presentation] 連結半単純コンパクトリー群に付随するゼータ関数について2010

    • Author(s)
      小森靖
    • Organizer
      2010年度表現論シンポジウム
    • Place of Presentation
      公共の宿おおとり荘
    • Year and Date
      2010-11-10
    • Related Report
      2013 Final Research Report
  • [Presentation] 連結半単純コンパクトリー群に付随するゼータ関数について2010

    • Author(s)
      小森靖
    • Organizer
      2010年度表現論シンポジウム
    • Place of Presentation
      静岡県公共の宿おおとり壮
    • Year and Date
      2010-11-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] ルート系のゼータ関数と多重ゼータ値I2010

    • Author(s)
      小森靖
    • Organizer
      多重ゼータ値の諸相
    • Place of Presentation
      京都大学
    • Year and Date
      2010-09-08
    • Related Report
      2013 Final Research Report 2010 Annual Research Report
  • [Presentation] Multiple Bernoulli polynomials and multiple L-functions of root systems2010

    • Author(s)
      Y. Komori
    • Organizer
      Developments in Quantum Integrable Systems
    • Place of Presentation
      京都大学
    • Year and Date
      2010-06-14
    • Related Report
      2013 Final Research Report 2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi