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Comprehensive study of multiple zeta functions and their application to quantum integrable systems

Research Project

Project/Area Number 17K05185
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionRikkyo University

Principal Investigator

Komori Yasushi  立教大学, 理学部, 教授 (80343200)

Project Period (FY) 2017-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords多重ゼータ関数 / ルート系
Outline of Final Research Achievements

Multiple zeta functions associated with root systems are studied by various methods for their special values and relations among them, and in particular, a description in terms of the generating functions is given as a unified viewpoint. Using this description, we can obtain a very large class of relations associated with each root system and its subroot systems. In addition, the theory has been developed by reexamining, simplifying, and improving the proofs of a large number of results obtained through previous research, and by incorporating new arguments and examples, we will publish a book that is easy to read even for beginners. I believe that this book will make a significant contribution to the development of the theory of zeta functions of root systems.

Academic Significance and Societal Importance of the Research Achievements

近年, 数論で最も重要な量のひとつであるゼータ関数と量子論で最も重要な量のひとつである分配関数とが結びついているという発見から新たな研究が生まれ、大きく発展し始めている. 本研究によって, 量子論やリー群を軸として広がりを見せている様々な多重ゼータ関数について, 分野を超えた広い枠組みで捉えることができ, 特殊値や関数関係式を通して多重ゼータ値の数論的理解や量子可積分系の基礎的な量の計算に貢献できたと考えている.

Report

(7 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (13 results)

All 2021 2020 2019 2018 2017

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 1 results) Presentation (6 results) (of which Int'l Joint Research: 1 results,  Invited: 5 results)

  • [Journal Article] Finite multiple zeta values, symmetric multiple zeta values and unified multiple zeta functions2021

    • Author(s)
      Komori Yasushi
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 73 Issue: 2 Pages: 221-255

    • DOI

      10.2748/tmj.20200226

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] A CONGRUENCE BETWEEN SYMMETRIC MULTIPLE ZETA-STAR VALUES AND MULTIPLE ZETA-STAR VALUES2021

    • Author(s)
      FUJITA Kento、KOMORI Yasushi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 75 Issue: 1 Pages: 149-167

    • DOI

      10.2206/kyushujm.75.149

    • NAID

      130008049829

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] An overview and supplements to the theory of functional relations for zeta-functions of root systems2020

    • Author(s)
      Komori Yasushi、Matsumoto Kohji、Tsumura Hirofumi
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 84 Pages: 263-295

    • DOI

      10.2969/aspm/08410263

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Zeta-functions of root systems and Poincare polynomials of Weyl groups2020

    • Author(s)
      Komori Yasushi、Matsumoto Kohji、Tsumura Hirofumi
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 72 Issue: 1 Pages: 87-126

    • DOI

      10.2748/tmj/1585101623

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] FINITE MULTIPLE ZETA VALUES, MULTIPLE ZETA FUNCTIONS AND MULTIPLE BERNOULLI POLYNOMIALS2018

    • Author(s)
      KOMORI Yasushi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 72 Issue: 2 Pages: 333-342

    • DOI

      10.2206/kyushujm.72.333

    • NAID

      130007521525

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Arakawa–Kaneko zeta-functions associated with <i>GL</i><sub>2</sub>(ℂ) and their functional relations2018

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

      Journal of the Mathematical Society of Japan

      Volume: 70 Issue: 1 Pages: 179-213

    • DOI

      10.2969/jmsj/07017501

    • NAID

      130006334063

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type2017

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

      RIMS Kokyuroku Bessatsu

      Volume: B68 Pages: 27-66

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] On variants of the Arakawa-Kaneko zeta function2021

    • Author(s)
      小森 靖
    • Organizer
      第3回 青葉山ゼータ研究集会
    • Related Report
      2020 Research-status Report
  • [Presentation] 有限多重ゼータ値, 対称多重ゼータ値, および補間ゼータ関数について2020

    • Author(s)
      小森 靖
    • Organizer
      多重ゼータ研究集会
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Finite Multiple Zeta Values, Symmetric Multiple Zeta Values and Unified Multiple Zeta Functions2019

    • Author(s)
      小森 靖
    • Organizer
      愛媛大学代数セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Finite Multiple Zeta Values, Multiple Zeta Functions and Multiple Bernoulli Polynomials2018

    • Author(s)
      小森 靖
    • Organizer
      九大多重ゼータセミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 多重楕円ガンマ関数の積分表示と関数関係式2018

    • Author(s)
      小森 靖
    • Organizer
      多重三角関数とその一般化
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Functional relations for zeta-functions of root systems and Poincare polynomials of Weyl groups I2017

    • Author(s)
      Y. Komori
    • Organizer
      Various Aspects of Multiple Zeta Functions
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2017-04-28   Modified: 2024-01-30  

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