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On the relation between infinite and finite places from the viewpoint of multiple zeta values over function fields

Research Project

Project/Area Number 18K13398
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 11010:Algebra-related
Research InstitutionUniversity of the Ryukyus (2019-2022)
Fukuoka Institute of Technology (2018)

Principal Investigator

Mishiba Yoshinori  琉球大学, 理学部, 助教 (70737725)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords多重ゼータ値 / 関数体 / 周期 / t加群 / tモチーフ / 線型独立性 / Carlitz多重ポリログ / 正標数 / 数論
Outline of Final Research Achievements

We studied infinite/v-adic multiple zeta values over function fields in positive characteristic, where v is a finite place of the function field. More precisely, we proved that the v-adic multiple zeta values satisfy the same algebraic relations that their corresponding infinite-adic multiple zeta values satisfy (joint work with Chieh-Yu Chang and Yen-Tsung Chen). We also studied the structure of the t-module, which is important in the above proof (joint work with Chang and Nathan Green). In addition, we determined the basis of the space of infintie-adic multiple zeta values (joint work with Chang and Chen).

Academic Significance and Societal Importance of the Research Achievements

無限進多重ゼータ値の間の代数的関係式がv進多重ゼータ値に伝播するという結果は,その証明手法が新しく,様々な拡張や応用があると考えられる.また,無限進多重ゼータ値が張る空間の基底の決定は,本分野における中心的な課題の一つであった.本結果により,無限進多重ゼータ値への理解が大きく進展したと考えられる.これらの結果の標数0における類似の問題は未解決であり,本研究の結果や証明の手法が,標数0への良い影響を与えると期待している.

Report

(6 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
  • Research Products

    (26 results)

All 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (9 results) Journal Article (3 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 3 results) Presentation (14 results) (of which Int'l Joint Research: 8 results,  Invited: 13 results)

  • [Int'l Joint Research] 国立清華大学(台湾)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Pennsylvania State University(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] 国立清華大学(台湾)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] 国立清華大学(台湾)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of California, San Diego(米国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] 国立清華大学(台湾)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of California, San Diego(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] 国立清華大学(台湾)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University of California, San Diego(米国)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Algebra structure of multiple zeta values in positive characteristic2022

    • Author(s)
      Chieh-Yu Chang, Yen-Tsung Chen, Yoshinori Mishiba
    • Journal Title

      Cambridge Journal of Mathematics

      Volume: 10 Issue: 4 Pages: 743-783

    • DOI

      10.4310/cjm.2022.v10.n4.a1

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Taylor coefficients of Anderson-Thakur series and explicit formulae2021

    • Author(s)
      Chieh-Yu Chang, Nathan Green, Yoshinori Mishiba
    • Journal Title

      Mathematische Annalen

      Volume: 379 Issue: 3-4 Pages: 1425-1474

    • DOI

      10.1007/s00208-020-02103-4

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On a conjecture of Furusho over function fields2021

    • Author(s)
      Chieh-Yu Chang, Yoshinori Mishiba
    • Journal Title

      Inventiones mathematicae

      Volume: 223 Issue: 1 Pages: 49-102

    • DOI

      10.1007/s00222-020-00988-1

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Thakur's basis conjecture for multiple zeta values in positive characteristic2023

    • Author(s)
      三柴善範
    • Organizer
      Number Theory in Tokyo
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On multiple zeta values over function fields and their linear independence2023

    • Author(s)
      三柴善範
    • Organizer
      第5回 青葉山ゼータ研究集会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Computations of multiple zeta values over function fields2023

    • Author(s)
      三柴善範
    • Organizer
      Computing Multiple Zeta Seminar
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Thakur's basis conjecture for multiple zeta values in positive characteristic2022

    • Author(s)
      三柴善範
    • Organizer
      2022 NCTS Workshop on Function Field Arithmetic
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On linear independence of multiple zeta values in positive characteristic2022

    • Author(s)
      三柴善範
    • Organizer
      多重ゼータ値の諸相
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 正標数交代多重ゼータ値が張る空間の生成元について2022

    • Author(s)
      三柴善範
    • Organizer
      2022早稲田整数論研究集会
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] On relations among v-adic multiple zeta values over function fields2021

    • Author(s)
      三柴善範
    • Organizer
      Japan Europe Number Theory Exchange Seminar
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Algebraic independence of certain Taylor coefficients of t-motivic multiple zeta values2020

    • Author(s)
      三柴善範
    • Organizer
      NCTS Seminar on Number Theory
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Logarithmic interpretation of Taylor coefficients of t-motivic multiple zeta values2020

    • Author(s)
      三柴善範
    • Organizer
      Japan-Taiwan joint workshop on multiple zeta values 2020
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Taylor coefficients of t-motivic multiple zeta values2019

    • Author(s)
      三柴善範
    • Organizer
      NCTS Seminar on Number Theory
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On Furusho's conjecture over function fields2019

    • Author(s)
      三柴善範
    • Organizer
      Arithmetic of Function Fields and Diophantine Geometry
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 正標数多重ゼータ値の対数表示2019

    • Author(s)
      三柴善範
    • Organizer
      東京電機大学数学講演会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] MZV's as Logarithms and Applications II2018

    • Author(s)
      三柴善範
    • Organizer
      Taiwan-Japan Joint Workshop on Multiple Zeta Values
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] On multiple zeta values over function fields and their algebraic independence2018

    • Author(s)
      三柴善範
    • Organizer
      九大多重ゼータセミナー
    • Related Report
      2018 Research-status Report
    • Invited

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Published: 2018-04-23   Modified: 2024-01-30  

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