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Research on number theoretic properties of zeta functions in several variables

Research Project

Project/Area Number 15K04788
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionTokyo Metropolitan University

Principal Investigator

TSUMURA Hirofumi  首都大学東京, 理工学研究科, 教授 (20310419)

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)
KOMORI Yasushi  立教大学, 理学部・数学科, 教授 (80343200)
FURUSHO Hidekazu  名古屋大学, 大学院・多元数理科学研究科, 准教授 (60377976)
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords整数論 / ゼータ関数 / 代数学
Outline of Final Research Achievements

The main aim in this research is to study what is called the zeta function which plays an important role in number theory and investigate their properties. In particular, we studied zeta functions in several variables mainly from the viewpoint of the analytic aspect. We studied the Witten zeta function in several variables which was defined based on Witten's work, and also the Arakawa-Kaneko zeta function defined by Tsuneo Arakawa and Masanobu Kaneko. Our main result is consider the number theoretic properties of these zeta functions,and consequently we obtained unknown properties of them and gave new results.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (13 results)

All 2018 2017 2016 2015 Other

All Journal Article (9 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 9 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (3 results) (of which Int'l Joint Research: 2 results,  Invited: 3 results) Remarks (1 results)

  • [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 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Double series identities arising from Jacobi's identity of the theta function2018

    • Author(s)
      Hirofumi Tsumura
    • Journal Title

      Results in Mathematics

      Volume: 73 Issue: 1 Pages: 1-12

    • DOI

      10.1007/s00025-018-0770-4

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fundamentals of p-adic multiple L-functions and evaluation of their special values2017

    • Author(s)
      Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
    • Journal Title

      Selecta Mathematica

      Volume: 23 Issue: 1 Pages: 39-100

    • DOI

      10.1007/s00029-016-0233-2

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Desingularization of complex multiple zeta-functions2017

    • Author(s)
      Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
    • Journal Title

      American Journal of Mathemtaics

      Volume: 139 Issue: 1 Pages: 147-173

    • DOI

      10.1353/ajm.2017.0002

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On multiple series of Eisenstein type2017

    • Author(s)
      H. Bachmann and H. Tsumura
    • Journal Title

      Ramanujan J.

      Volume: 42 Issue: 2 Pages: 470-489

    • DOI

      10.1007/s11139-015-9738-0

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebras V2015

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

      Glasg. Math. J

      Volume: 57 Issue: 1 Pages: 107-130

    • DOI

      10.1017/s0017089514000160

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Infinite series involving hyperbolic functions2015

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

      Lith. Math. J.

      Volume: 55 Pages: 102-118

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Zeta-functions of weight lattices of compact connected semisimple Lie groups2015

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

      Siauliai Math. Semin.

      Volume: 10(18) Pages: 149-179

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Mean value theorems for the double zeta-function2015

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

      Journal of the Mathematical Society of Japan

      Volume: 67 Issue: 1 Pages: 383-406

    • DOI

      10.2969/jmsj/06710383

    • NAID

      130004927755

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] Functional relations for zeta-functions of root systems and Poincare polynomials of Weyl groups2017

    • Author(s)
      Hirofumi Tsumura
    • Organizer
      Various Aspects of Multiple Zeta Functions
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多重ベルヌーイ数に関する最近の話題2016

    • Author(s)
      津村博文
    • Organizer
      大分整数論研究集会
    • Place of Presentation
      サテライトキャンパスおおいた
    • Year and Date
      2016-10-08
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Desingularization of complex multiple zeta-functions and construction of p-adic multiple L-functions2015

    • Author(s)
      H. Tsumura
    • Organizer
      The conference of Zeta Functions of Several Variables and Applications
    • Place of Presentation
      名古屋大学
    • Year and Date
      2015-11-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] 首都大学東京HP

    • URL

      http://www.tmu.ac.jp/stafflist/data/ta/635.html

    • Related Report
      2016 Research-status Report 2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2019-03-29  

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