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The analytic theory of arithmetic L-functions and multiple zeta-functions

Research Project

Project/Area Number 18H01111
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionNagoya University

Principal Investigator

Matsumoto Kohji  名古屋大学, 多元数理科学研究科, 教授 (60192754)

Co-Investigator(Kenkyū-buntansha) 見正 秀彦  東京電機大学, システムデザイン工学部, 教授 (10435456)
鈴木 正俊  東京工業大学, 理学院, 准教授 (30534052)
小森 靖  立教大学, 理学部, 教授 (80343200)
Project Period (FY) 2018-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥14,560,000 (Direct Cost: ¥11,200,000、Indirect Cost: ¥3,360,000)
Fiscal Year 2021: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2019: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2018: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Keywordsゼータ関数 / L 関数 / 多重ゼータ関数 / 値分布 / ルート系 / 普遍性 / M 関数 / 普遍性定理 / L関数 / 実零点 / 漸近挙動 / 特殊値 / 離散普遍性 / 混合普遍性 / ルート系のゼータ関数 / Schur 多重ゼータ関数 / 関数関係式 / 明示公式 / 周期積分 / Hurwitz ゼータ関数
Outline of Final Research Achievements

We studied mainly analytic aspects of zeta-functions, L-functions and multiple zeta-functions which are quite important in number theory. As for the value-distribution of zeta-functions, we used the techniques of probability theory and function-space theory to obtain new type of limit theorems and universality theorems, and further, considered connections with Dirichlet series attached to Goldbach's problem. On multiple zeta-functions, we also based on the aspects of representation theory and combinatorics to find connections between Schur multiple zeta-functions and zeta-functions of root systems.

Academic Significance and Societal Importance of the Research Achievements

ゼータ関数、多重ゼータ関数の研究は今も世界中で極めて活発に行われており、特に解析学や表現論などの幅広い枠組みでの研究は新しい研究方向を切り開く可能性が高いと考えられる。純理論的な数学の研究なので、直接的な社会へのフィードバックはすぐには見出せないが、学術の活性化を通じて社会の高度化にも生かされることになるはずだと考える。

Report

(5 results)
  • 2022 Final Research Report ( PDF )
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (55 results)

All 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (10 results) Journal Article (22 results) (of which Int'l Joint Research: 10 results,  Peer Reviewed: 22 results,  Open Access: 1 results) Presentation (22 results) (of which Int'l Joint Research: 14 results,  Invited: 22 results) Book (1 results)

  • [Int'l Joint Research] Magnus Vitautas University(リトアニア)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] University of Novi Sad(セルビア)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Universite de Lyon(フランス)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Universitaet Linz(オーストリア)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Novi Sad Univ(セルビア)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Lille 大学/Lyon 大学(フランス)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Vytautas Magnus 大学(リトアニア)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Linz 工科大学(オーストリア)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Univ Lyon(フランス)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Vytautas Magnus Univ(リトアニア)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] A survey of the theory of mixed joint universality for zeta-functions2022

    • Author(s)
      R. Kacinskaite and K. matsumoto
    • Journal Title

      Number Theory, Walter de Gruyter

      Volume: 1 Pages: 47-60

    • DOI

      10.1515/9783110761115-004

    • ISBN
      9783110761115
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Expressions of Schur multiple zeta-functions of anti-hook type by zeta-functions of root systems2021

    • Author(s)
      Kohji Matsumoto and Maki Nakasuji
    • Journal Title

      Publ. Math. Debrecen

      Volume: 98 Issue: 3-4 Pages: 345-377

    • DOI

      10.5486/pmd.2021.8869

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Values of multiple zeta functions with polynomial denominators at non-positive integers2021

    • Author(s)
      Driss essouabri and Kohji Matsumoto
    • Journal Title

      Intern. J. Math.

      Volume: 32 Issue: 06 Pages: 2150038-2150038

    • DOI

      10.1142/s0129167x21500385

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The discrete case of the mixed joint universality for a class of certain partial zeta-functions2021

    • Author(s)
      Roma Kacinskaite and Kohji Matsumoto
    • Journal Title

      Taiwanese J. Math.

      Volume: 25 Issue: 4

    • DOI

      10.11650/tjm/210201

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An asymptotic formula for the 2𝑘-th power mean value of |(𝐿′/𝐿)(1 + 𝑖𝑡<sub>0</sub>, 𝜒)|2021

    • Author(s)
      Kohji Matsumoto ans Sumaia Saad Eddin
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 73 Issue: 3 Pages: 781-814

    • DOI

      10.2969/jmsj/79987998

    • NAID

      130008067984

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A survey on the theory of multiple Dirichlet series with arithmetical coefficients as numerators2021

    • Author(s)
      Kohji Matsumoto
    • Journal Title

      Lithuanian Math.J.

      Volume: 61 Issue: 3 Pages: 391-400

    • DOI

      10.1007/s10986-021-09534-9

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Double Dirichlet series associated with arithmetic functions2021

    • Author(s)
      Kohji Matsumoto, Akihiko Nawashiro and Hirofumi tTumura
    • Journal Title

      Kodai Math. J.

      Volume: 44

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An M-function associated with Goldbach's problem2021

    • Author(s)
      Kohji Matsumoto
    • Journal Title

      J. Ramanujan Math. Soc.

      Volume: 36

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the behavior of multiple zeta-functions with identical arguments on the real line2021

    • Author(s)
      Matsumoto Kohji、Matsusaka Toshiki、Tanackov Ilija
    • Journal Title

      Journal of Number Theory

      Volume: - Pages: 151-182

    • DOI

      10.1016/j.jnt.2021.11.008

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Values at non-positive integers of generalized Euler-Zagier multiple zeta-functions2020

    • Author(s)
      D. Essouabri and K. Matsumoto
    • Journal Title

      Acta Arith.

      Volume: 193 Pages: 109-131

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Zeta-functions of root systems and Poincare polynomials of Weyl groups2020

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

      Tohoku Math J.

      Volume: 72 Pages: 87-126

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An overview and supplements to the theory of functional relations for zeta-functions of root systems2020

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

      Adv. Stud. Pure Math.

      Volume: 84 Pages: 263-295

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical computations on the zeros of the Euler double zeta-functions II2020

    • Author(s)
      K. Matsumoto and M. Shoji
    • Journal Title

      European J. Math.

      Volume: 6 Pages: 488-507

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Laurent series expansions of multiple zeta-functions of Euler-Zagier type at integer points2020

    • Author(s)
      K. Matsumoto, T. Onozuka and I. Wakabayashi
    • Journal Title

      Math. Z.

      Volume: 295 Pages: 623-642

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On mixed joint discrete universality for a class of zeta-functions: a further generalization2020

    • Author(s)
      R. Kacinskaite and K. Matsumoto
    • Journal Title

      Math. Modell. Anal.

      Volume: 25 Pages: 569-583

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the value-distribution of symmetic power L-functions2020

    • Author(s)
      K. Matsumoto and Y. Umegaki
    • Journal Title

      Ramanujan Math. Soc. Lecture Notes

      Volume: 26 Pages: 147-167

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the density function for the value-distribution of automorphic L-functions2019

    • Author(s)
      K. Matsumoto and Y. Umegaki
    • Journal Title

      J. Number Theory

      Volume: 198 Pages: 176-199

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On mixed joint discrete universality for a class of zeta-functions II2019

    • Author(s)
      R. Kacinskaite and K. Matsumoto
    • Journal Title

      Lith. Math. J.

      Volume: 59 Issue: 1 Pages: 54-66

    • DOI

      10.1007/s10986-019-09432-1

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Values at non-positive integers of partially twisted multiple zeta-functions I2019

    • Author(s)
      D. Essouabri and K. Matsumoto
    • Journal Title

      Comment. Math. Univ. St. Pauli

      Volume: 67 Pages: 83-100

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] ゼータ関数の普遍性について2019

    • Author(s)
      松本耕二
    • Journal Title

      応用数理

      Volume: 29 Pages: 135-139

    • NAID

      130007775880

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET L-FUNCTIONS2018

    • Author(s)
      Bhowmik Gautami、Halupczok Karin、Matsumoto Kohji、Suzuki Yuta
    • Journal Title

      Mathematika

      Volume: 65 Issue: 1 Pages: 57-97

    • DOI

      10.1112/s0025579318000323

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the value-distribution of the difference between logarithms of two symmetric power L-functions2018

    • Author(s)
      K. Matsumoto and Y. Umegaki
    • Journal Title

      International Journal of Number Theory

      Volume: 14 Pages: 2045-2081

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] The theory of multiple zeta-functions: the history and recent developments2023

    • Author(s)
      Kohji Matsumoto
    • Organizer
      Algebraic and Analytic Aspects of L-functions, Incheon, Korea
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dirichlet series related with Goldbach counting functions --- the classical case and the function-field analogue2023

    • Author(s)
      Kohji Matsumoto
    • Organizer
      Algebraic and Analytic Aspects of L-functions, Incheon, Korea
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多重ゼータ関数の実軸上での挙動について2022

    • Author(s)
      松本耕二
    • Organizer
      第16回多重ゼータ研究集会&第58回関西多重ゼータ研究会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] M-functions associated with cusp forms2022

    • Author(s)
      Kohji Matsumoto
    • Organizer
      !st Intern Workshop in Analytic Number tehory at UNIST, Korea
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The theory of multiple zeta-functions: The history and recent developments2022

    • Author(s)
      kohji Matsumoto
    • Organizer
      Lithuanian Mathematical Society
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On Schur multiple zeta functions2022

    • Author(s)
      Kohji Matsumoto
    • Organizer
      ELAZ 2022, Poznan, Poland
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 対称べき L 関数の対数のレベルに関する値分布について2022

    • Author(s)
      松本耕二
    • Organizer
      「解析的整数論とその周辺」研究集会、京都大学
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] 数論的関数を分子に持つ二重 Dirichlet 級数について2022

    • Author(s)
      松本耕二
    • Organizer
      第60回関西多重ゼータ研究会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Multiple Dirichlet series with arithmetical coefficients on the numerators2020

    • Author(s)
      K. Matsumoto
    • Organizer
      IMSc Webinar, IMS, Chennai, India
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] An M-function associated with Goldbach's problem2020

    • Author(s)
      K. Matsumoto
    • Organizer
      Intern. Conf. on Number Theory and Discrete Math., Kochi, India
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the behavior of multiple zeta-functions with identical arguments on the real line2020

    • Author(s)
      K. Matsumoto
    • Organizer
      Balu Fest, IMSc, Chennai, India
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多重ゼータ関数の負の整数点での値の表示について2020

    • Author(s)
      松本耕二
    • Organizer
      第13回多重ゼータ研究集会&第48回関西多重ゼータ研究会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Multiple Dirichlet series with arithmetical coefficients on the numerators2019

    • Author(s)
      Kohji Matsumoto
    • Organizer
      Mini-Symposium on Analytic Number Theory and Applications
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多重ゼータ関数の零点集合の形状について2019

    • Author(s)
      松本耕二
    • Organizer
      東工大数論・幾何学セミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On the zero-sets of multiple zeta-functions2019

    • Author(s)
      Kohji Matsumoto
    • Organizer
      Fonctions Zeta
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] \zeta^2(s) の近似関数等式の誤差項の平均値について2019

    • Author(s)
      松本耕二
    • Organizer
      整数論・環論合同セミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Asymptotic results on mean values of logarithmic derivatives of Dirichlet L-functions2019

    • Author(s)
      K. Matsumoto
    • Organizer
      Conference in Number Theory
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An overview of the theory of multiple zeta-functions2019

    • Author(s)
      K. Matsumoto
    • Organizer
      Value distribution of zeta and L-functions and related topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Values of general multiple zeta-functions with polynomial denominators at non-positive integer points2019

    • Author(s)
      K. Matsumoto
    • Organizer
      Value distribution of zeta and L-functions and related topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the theory of M-functions2018

    • Author(s)
      K. Katsumoto
    • Organizer
      Profinite monodromy, Galois representations, and complex functions
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ゼータ関数の普遍性について2018

    • Author(s)
      K. Matsumoto
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On density functions in the value-distribution theory of L-functions2018

    • Author(s)
      K. Matsumoto
    • Organizer
      International Conference on Number Theory dedicated to the 70th birthdays of Professors A. Laurincikas and E. Manstavicius
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Book] ルート系のゼータ関数の理論入門2018

    • Author(s)
      松本耕二
    • Total Pages
      58
    • Publisher
      東北大学大学院理学研究科
    • Related Report
      2018 Annual Research Report

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

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