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Functional equations for zeta-functions and Euler product

Research Project

Project/Area Number 25400032
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KANEMITSU Shigeru  近畿大学, 工学部, 教授 (60117091)

Co-Investigator(Kenkyū-buntansha) TSUKADA Haruo  近畿大学, 産業理工学部, 教授 (00257990)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Keywordsゼータ関数 / 関数等式 / モジュラー関係式 / イーワルド展開 / 非加工モジュラー関係式 / シータ変換公式 / モジュラーリレイション / 特殊関数 / H-関数 / オイラー積 / 零点分布 / フォックスH-関数 / マイヤーG-関数 / ベータ変換 / 超幾何関数変換
Outline of Final Research Achievements

The main achievement of our research is the completion of the book ``Contributions to the theory of zeta-functions--modular relation supremacy'' which has been the ultimate objective of this series of research under the support of the JSPS grant. The book elucidate all existing identities equivalent or consequences of the functions equation--zeta symmetry. We have made clear the threshold between the zeta-function with Euler product and without. We are reay to launching on Vol. 2 in which we will work with zets with Euler product.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (20 results)

All 2015 2014 2013 Other

All Int'l Joint Research (3 results) Journal Article (8 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 8 results,  Acknowledgement Compliant: 4 results,  Open Access: 1 results) Presentation (6 results) (of which Int'l Joint Research: 2 results,  Invited: 6 results) Book (3 results)

  • [Int'l Joint Research] Harish-Chadra Institute(India)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Polish Academy of Sciences(Poland)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Weinan Normal university(China)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] On congruences for certain sums of E. Lehmer's type2015

    • Author(s)
      S. Kanemitsu, T. Kuzumaki, J. Urbanowicz
    • Journal Title

      Acta Arith.

      Volume: 37 Pages: 1-28

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On modular relations2015

    • Author(s)
      T. Arai, K. Chakraborty, S. Kanemitsu
    • Journal Title

      Proc. seventh China-Japan Sem. Number Theory

      Volume: 1 Pages: 1-64

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Applications of the beta-transform2015

    • Author(s)
      K. Xhakraborty, S. Kanemitsu, H. Tsukada
    • Journal Title

      Siaulai Math. Sem.

      Volume: 10 Pages: 5-28

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The quadratic reciprocity and Riemann’s non-differentiable function2015

    • Author(s)
      K. Chakraborty, S. Kanemitsu, H. -L. Li
    • Journal Title

      Res. Number Theory

      Volume: 1:14 Pages: 1-8

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the Barnes multiple zeta- and gamma function2014

    • Author(s)
      K. Chakraborty,S. Kanemitsu and  T. Kuzumaki
    • Journal Title

      Siaulai Math. Sem.

      Volume: 9 Pages: 27-41

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Matrices for finite abelian groups, finite Fourier transforms and codes2013

    • Author(s)
      S. Kanemitsu and M. Waldschmidt
    • Journal Title

      Proc. 6th China-Japan Sem. Number Theory, World Sci.

      Volume: 8 Pages: 90-106

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Circulants, linear recurrences and codes2013

    • Author(s)
      L. Jiang,S. Kanemitsu and H. Kitajima
    • Journal Title

      Ann. Univ. Sci. Budapest . Eotvos Sect. Comput.

      Volume: 40 Pages: 363-377

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Arithmetical class number formula for certain quadratic fields2013

    • Author(s)
      K. Chakraborty S. Kanemitsu and T. Kuzumaki
    • Journal Title

      Hardy-Ramanujan J.

      Volume: 36 Pages: 1-7

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Special functions in number theory and science2015

    • Author(s)
      S. Kanemitsu
    • Organizer
      International Conf. Special Functions
    • Place of Presentation
      Delhi, India
    • Year and Date
      2015-09-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Special functions in number theory2015

    • Author(s)
      S. Kanemitsu
    • Organizer
      Huizhou University Colloq.
    • Place of Presentation
      Huizhou, China
    • Year and Date
      2015-08-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quadratic reciprocity and Riemann's non-differentiable function2015

    • Author(s)
      S. Kanemitsu
    • Organizer
      Baoji Meeting on Number Theory
    • Place of Presentation
      Baoji Jianguo Hotel (中国)
    • Year and Date
      2015-03-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Evaluation of the probability integral2015

    • Author(s)
      S. Kanemitsu
    • Organizer
      Weinan Normal University Colloquium
    • Place of Presentation
      Weinan Normal University (中国)
    • Year and Date
      2015-03-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On linearized product of two zeta-functions2014

    • Author(s)
      S. Kanemitsu
    • Organizer
      10th Intern. Number Th. conf.
    • Place of Presentation
      Xinyuan Intern. H.Luoyang, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A remark on Kummer’s conjecture2013

    • Author(s)
      J. J. Urroz
    • Organizer
      Conf. analytic theory of automor. forms
    • Place of Presentation
      Inst. MatSci. (Chennai), India
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] Plowing and starring through high wave forms—Proc. of the 7th China-Japan Seminar on number theory2015

    • Author(s)
      M. Kaneko, S. Kanemitsu, J. -Y. Liu
    • Total Pages
      191
    • Publisher
      World Scientific
    • Related Report
      2015 Annual Research Report
  • [Book] Abridging over Troubled Water---Scientific Foundation of Engineering Subjects2015

    • Author(s)
      S. Kanemitsu, H.-L Li, N.-L. Wang
    • Total Pages
      54
    • Publisher
      Science Publishing Group
    • Related Report
      2015 Annual Research Report
  • [Book] Contributions to the theory of zeta-functions---modular relation supremacy2014

    • Author(s)
      S. Kanemitsu and H. Tsukada
    • Total Pages
      303
    • Publisher
      World Scientific (シンガポール‐イギリス)
    • Related Report
      2014 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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