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The outlook for the dimension conjecture and the study of Lie algebras of multiple zeta values and multiple Eisenstein series

Research Project

Project/Area Number 18K13393
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 11010:Algebra-related
Research InstitutionAichi Prefectural University

Principal Investigator

Tasaka Koji  愛知県立大学, 情報科学部, 講師 (30780762)

Project Period (FY) 2018-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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)
Keywords多重ゼータ値 / モジュラー形式 / 多重モジュラー値 / 多重Eisenstein級数 / 複シャッフルリー代数 / Broadhurst-Kreimer予想 / モチビックLie代数
Outline of Final Research Achievements

We study a conjecture proposed by Broadhurst and Kreimer in 1997 stating mysterious relationships between multiple zeta values (real numbers) and modular forms (holomorphic function on the complex upper-half plane). One of the upshots of this project is a newly analytic interpretation of the so-called "modular relation (an explicit correspondence between double zeta values and modular forms)", which was first established by Gangl, Kaneko and Zagier in 2006.

Academic Significance and Societal Importance of the Research Achievements

近年,モジュラー関係式を一つの動機として,多重ゼータ値とモジュラー形式を共通の枠組みで捉える研究がヨーロッパを中心にいくつかおこっている。世界的な視点では,むしろ幾何的な方面からのアプローチが盛んであるが,本研究では内在する組合せ的な構造やモジュラー形式の解析理論などに新しい貢献ができたという点において,有意義である。

Report

(3 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • Research Products

    (22 results)

All 2020 2019 2018 Other

All Journal Article (4 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 4 results,  Open Access: 3 results) Presentation (16 results) (of which Int'l Joint Research: 3 results,  Invited: 1 results) Remarks (2 results)

  • [Journal Article] Hecke eigenform and double Eisenstein series2020

    • Author(s)
      KOJI TASAKA
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 148 Issue: 1 Pages: 53-58

    • DOI

      10.1090/proc/14680

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products2019

    • Author(s)
      Nils Matthes, Koji Tasaka
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 73 Pages: 337-356

    • NAID

      130007871386

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Hecke eigenform and double Eisenstein series2019

    • Author(s)
      Tasaka Koji
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products2019

    • Author(s)
      Nils Matthes、Tasaka Koji
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 印刷中

    • NAID

      130007871386

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] 有限多重ゼータ値とその応用2020

    • Author(s)
      田坂浩二
    • Organizer
      第18回量子情報ミニワークショップ
    • Related Report
      2019 Annual Research Report
  • [Presentation] 有限多重調和級数の1の冪根での値と有限および対称多重ゼータ値2019

    • Author(s)
      バッハマンヘンリク, 竹山美宏,田坂浩二
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Finite and symmetric colored multiple zeta values2019

    • Author(s)
      Koji Tasaka
    • Organizer
      RIMS conference "Various Aspects on Multiple Zeta Values"
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 様々な多重ゼータ値の関係について2019

    • Author(s)
      田坂浩二
    • Organizer
      近畿大学談話会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Toy models of double shuffle Lie algebra2019

    • Author(s)
      田坂浩二
    • Organizer
      信州トポロジーセミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] Hecke固有形式と2重Eisenstein級数2019

    • Author(s)
      田坂浩二
    • Organizer
      2019年日本数学会年会
    • Related Report
      2018 Research-status Report
  • [Presentation] Period polynomial relations for double zeta values2019

    • Author(s)
      田坂浩二
    • Organizer
      第12回ゼータ若手研究集会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] ヘッケ固有形式と2重アイゼンシュタイン級数2019

    • Author(s)
      田坂浩二
    • Organizer
      第12回東京電機大学数学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] レベル付き2重ゼータ値のモジュラー関係式について2018

    • Author(s)
      田坂浩二
    • Organizer
      関西多重ゼータ研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] The Gangl-Kaneko-Zagier relation and the Ihara-Takao relation2018

    • Author(s)
      Koji Tasaka
    • Organizer
      Kyushu multi-zeta seminar
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Broadhurst-Kreimer予想について2018

    • Author(s)
      田坂浩二
    • Organizer
      第26回整数論サマースクール
    • Related Report
      2018 Research-status Report
  • [Presentation] Multiple zeta values and modular forms2018

    • Author(s)
      Koji Tasaka
    • Organizer
      Taiwan-Japan Joint Workshop on Multiple Zeta Values
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Anatomical decomposition of zeta elements2018

    • Author(s)
      田坂浩二
    • Organizer
      慶應義塾大学 代数セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] 4点抜き射影直線上の反復積分の和公式2018

    • Author(s)
      田坂浩二
    • Organizer
      名古屋大学 解析数論セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] 多重ゼータ値と複シャッフルリー代数の極化2018

    • Author(s)
      田坂浩二
    • Organizer
      九大多重ゼータセミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] 様々な多重ゼータ値の統一理論に向けて2018

    • Author(s)
      田坂浩二
    • Organizer
      愛知数論セミナー
    • Related Report
      2018 Research-status Report
  • [Remarks] 田坂浩二のHP

    • URL

      http://www.ist.aichi-pu.ac.jp/~tasaka/

    • Related Report
      2019 Annual Research Report
  • [Remarks] 田坂浩二のwebページ

    • URL

      http://www.ist.aichi-pu.ac.jp/~tasaka/

    • Related Report
      2018 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2021-02-19  

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