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Fox functions and zeta-functions

Research Project

Project/Area Number 21540029
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKinki University

Principal Investigator

KANEMITU Shigeru  近畿大学, 産業理工学部, 教授 (60117091)

Co-Investigator(Kenkyū-buntansha) TSUKADA Haruo  近畿大学, 産業理工学部, 教授 (00257990)
Co-Investigator(Renkei-kenkyūsha) TANIGAWA Yoshio  名古屋大学, 大学院・多元数理科学研究科, 准教授 (50109261)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywordsゼータ関数 / 関数等式 / モジュラー関係式 / フーリエ級数 / 超幾何級数 / プラナ和公式 / 超幾何関数 / 短区間指標和 / エプシュタインゼータ関数 / アイゼンシュタインの等式 / オイラー積 / フリウィッツゼータ関数 / デデキンドイータ関数 / パーセヴァル等式 / フォックス関数
Research Abstract

The purpose of the present research is to locate all the identities that have been assembled in the last 150 years after Riemann, equivalent to the functional equation for a wide class of zeta-functions in terms of Fox H-functions and by locating them in terms of the Meijer G-functions, to find new identities that are useful not only in mathematics but also in other scientific disciplines. In the year 2011, we were able to accomplish this task in the following setting : the origin of Plana's summation formula, the formula for short interval character sums and arithmetical Fourier series

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (47 results)

All 2011 2010 2009 Other

All Journal Article (30 results) (of which Peer Reviewed: 30 results) Presentation (11 results) Book (6 results)

  • [Journal Article] On arithmetical Fourier series and the modular relation2011

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

      Kyushu J. Math

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On some new congruences for generalized Bernoulli numbers2011

    • Author(s)
      S. Kanemitsu, J. Urbanowicz and N.-L. Wang
    • Journal Title

      Acta Arith

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Weber-Fechner law2011

    • Author(s)
      K. Takahashi, T. Hasegawa, G. Hirano, T. Kaida S. Kanemitsuand H. Tsukada
    • Journal Title

      Siaulai Math

      Volume: 6 Pages: 85-91

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Plana's summation formula as a modular relation and applications2011

    • Author(s)
      H.-L. Li, S. Kanemitsuand X.-H. Wang
    • Journal Title

      Int. Transf. Special Functions

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetical identities and zeta-functions2011

    • Author(s)
      S. Kanemitsu, J. Ma and Y. Tanigawa
    • Journal Title

      Math. Nachr

      Volume: 284 Pages: 287-297

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The modular relation and the Euler digamma function2011

    • Author(s)
      K. Chakraborty, S. Kanemitsu and X.-H. Wang
    • Journal Title

      Kyushu J. Math

      Volume: 65 Pages: 39-53

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted short-interval character sums2011

    • Author(s)
      S. Kanemitsu, H.-L. Li and N.-L. Wang
    • Journal Title

      Proc. Amer. Math. Soc

      Volume: 139 Pages: 1521-1532

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted short-interval character sums2011

    • Author(s)
      S.Kanemitsu, H.-L.Li, N.-L.Wang
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 139 Pages: 1521-1532

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The modular relation and the Euler digamma function2011

    • Author(s)
      K.Chakraborty, S.Kanemitsu, X.-H.Wang
    • Journal Title

      Kyushu J.Math.

      Volume: 65 Pages: 39-53

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetical identities and zeta-functions2011

    • Author(s)
      S.Kanemitsu, J.Ma, Y.Tanigawa
    • Journal Title

      Math.Nachr.

      Volume: 284 Pages: 287-297

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Plana's summation formula as a modular relation and applications2011

    • Author(s)
      S.Kanemitsu, H.-L.Li, X.-H.Wang
    • Journal Title

      Int.Transf, Special Functions

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Weber-Fechner law2011

    • Author(s)
      S.Kanemitsu, H.-L.Li, X.-H. Wang
    • Journal Title

      Siaulai Math.Sem.

      Volume: 6 Pages: 85-91

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Structural elucidation of Eisenstein's formula2010

    • Author(s)
      S. Kanemitsu, H.-L. Li and M. Hashimoto
    • Journal Title

      Sci. China

      Volume: 53 Pages: 2341-2350

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The legacy of Alladi Ramakrishnan in the mathematical sciences2010

    • Author(s)
      S. Kanemitsu and H. Tsukada
    • Journal Title

      K. Alladi, J. Klauder, C. R. Rao, Springer

      Pages: 275-292

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the values of a class of Dirichlet series at rational arguments2010

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

      Proc. Amer. Math. Soc

      Volume: 138 Pages: 1223-1230

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Square-free integers as ideal norms2010

    • Author(s)
      S. Kanemitsu, A. Laurinchikas and J. Ma
    • Journal Title

      Acta Math. Sinica

      Volume: 26 Pages: 621-628

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Square-free integers as ideal norms2010

    • Author(s)
      S.Kanemitsu, Laurinchikas, J.Ma
    • Journal Title

      Acta Math.Sinica

      Volume: 26 Pages: 621-628

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the values of a class of Dirichlet series at rational arguments2010

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

      Proc.Amer.Math.Soc

      Volume: 138 Pages: 1223-1230

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Structural elucidation of Eisenstein's formula2010

    • Author(s)
      H.-L.Li, M.Hashimoto, S.Kanemitsu
    • Journal Title

      Sci.China

      Volume: 53 Pages: 2341-2350

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Crystal symmetry and zeta symmetry2010

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

      The legacy of Alladi Ramakrishan, Springer Verl.

      Pages: 275-292

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite expressions for higher derivatives of the Dirichlet$ L$-function and the Deninger$ R$-function2009

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

      Hardy-Ramanujan J

      Volume: 32 Pages: 38-53

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Transformation formulas for Lambert series2009

    • Author(s)
      S. Kanemitsuand T. Kuzumaki
    • Journal Title

      Siaulai Math

      Volume: 4 Pages: 105-123

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Manifestations of the Parseval identity2009

    • Author(s)
      K. Chakraborty, S. Kanemitsu, J.-H. Li and X.-H. Wang
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci.

      Volume: 85 No.9 Pages: 149-154

    • NAID

      40016869171

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Examples of the Hurwitz transform2009

    • Author(s)
      M Hashimoto, S. Kanemitsu and H.-L. Li
    • Journal Title

      J. Math. Soc. Japan

      Volume: 61 Pages: 651-660

    • NAID

      10026998385

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the discrete mean value of the product of two Dirichlet L-functions2009

    • Author(s)
      S. Kanemitsu, J. Ma and W.-P. Zhang
    • Journal Title

      Abh. Math

      Volume: 79 Pages: 149-164

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Examples of the Hurwitz transform2009

    • Author(s)
      Li, 橋本, 金光
    • Journal Title

      J.Math.Soc.Japan 61

      Pages: 651-660

    • NAID

      10026998385

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Transformation formulas for Lambert series2009

    • Author(s)
      金光, 葛巻
    • Journal Title

      Siaulai Math, Sem. 4

      Pages: 105-123

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Manifestatiosn of the Parseval identity2009

    • Author(s)
      Chakraborty, 金光, Li, Wang
    • Journal Title

      Proc.Japan Acad. 85

      Pages: 149-154

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the discrete mean value of the product of two Dirichlet L-functions2009

    • Author(s)
      金光, Ma, Zhang
    • Journal Title

      Abh.Math.Sem.Univ.Hamburg 79

      Pages: 149-164

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite expressions for higher derivatives of the Dirichlet $L$-function and the Deninger $R$-funtion2009

    • Author(s)
      Chakraborty, 金光, 葛巻
    • Journal Title

      Hardy-Ramanujan J. 32

      Pages: 38-53

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Some applications of circulant matrices2011

    • Author(s)
      金光滋
    • Organizer
      第6回日中数論セミナー上海交通大学
    • Place of Presentation
      上海
    • Year and Date
      2011-08-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Some applications of circulant matrices2011

    • Author(s)
      S.Kanemitsu
    • Organizer
      The 6^<th> China-Japan Sem.on Number Th
    • Place of Presentation
      Shanghai Jiaoton Univ.
    • Year and Date
      2011-08-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] On the Weber-Fechner law2011

    • Author(s)
      金光滋
    • Organizer
      渭南師範学院数学系講演会
    • Place of Presentation
      中国・渭南
    • Year and Date
      2011-03-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Iterates of functions, RH and the Weber-Fechner law2011

    • Author(s)
      金光滋
    • Organizer
      商洛師範学院数学系講演会
    • Place of Presentation
      中国,商洛
    • Year and Date
      2011-03-23
    • Related Report
      2011 Final Research Report
  • [Presentation] Exhausting the two principles in number theory2011

    • Author(s)
      金光滋
    • Organizer
      アブダスサラム数理科学校GC Univ, Lahoreセミナー
    • Place of Presentation
      パキスタン
    • Year and Date
      2011-02-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Exhausting the two principles in number theory2011

    • Author(s)
      S.Kanemitsu
    • Organizer
      Abudas Salam School of math.sci, Sem.
    • Place of Presentation
      The GC Univ., Lahore
    • Year and Date
      2011-02-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] On multiplicative functions associated with a pair of cusp formsアブダスサラム数理科学校GC Univ, Lahoreにおける2011

    • Author(s)
      金光滋
    • Organizer
      第5回21世紀数学国際会
    • Place of Presentation
      パキスタン
    • Year and Date
      2011-02-10
    • Related Report
      2011 Final Research Report
  • [Presentation] On multiplicative functions associated with a pair of cusp forms2011

    • Author(s)
      S.Kanemitsu
    • Organizer
      The 5^<th> intern.Conf.on the 21^<st> century math., Abudas Salam School of math.sci.
    • Place of Presentation
      The GC Univ., Lahore
    • Year and Date
      2011-02-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] L' estro armonico del circolo di Euler-Gauss-Dirichlet-Riemann2010

    • Author(s)
      金光滋
    • Organizer
      カトマンズ大学におけるCIMPA School
    • Place of Presentation
      ネパール
    • Year and Date
      2010-07-28
    • Related Report
      2011 Final Research Report
  • [Presentation] The Riemann zeta-function and the Karman vortex street2010

    • Author(s)
      金光滋
    • Organizer
      渭南師範学院数学系セミナー平成
    • Place of Presentation
      中国,渭南
    • Year and Date
      2010-03-18
    • Related Report
      2011 Final Research Report
  • [Presentation] L'estro armonico del circolo di Euler-Gauss-Dirichlet-Riemann

    • Author(s)
      S.Kanemitsu
    • Organizer
      CIMPA School in Kathmandu
    • Place of Presentation
      Kathmandu Univ.
    • Related Report
      2010 Annual Research Report
  • [Book] 数論未解決問題の事典2010

    • Author(s)
      金光滋
    • Total Pages
      414
    • Publisher
      朝倉書店
    • Related Report
      2011 Final Research Report
  • [Book] 数論未解決問題の事典2010

    • Author(s)
      R.Kガイ(金光滋訳)
    • Total Pages
      414
    • Publisher
      朝倉書店
    • Related Report
      2010 Annual Research Report
  • [Book] Dreaming in dreams-Pro. of the 4th China-Japan Seminar on number theory held at Kinki University, Higashi-osaka, Japan2009

    • Author(s)
      S. Kanemitsuand J.-Y. Liu
    • Total Pages
      278
    • Related Report
      2011 Final Research Report
  • [Book] Vistas of special functions II2009

    • Author(s)
      K. Chakraborty, S. Kanemitsuand H. Tsukada
    • Total Pages
      278
    • Related Report
      2011 Final Research Report
  • [Book] Vistas of special functions II2009

    • Author(s)
      Chakraborty, 金光, 塚田
    • Total Pages
      272
    • Publisher
      World Scientific
    • Related Report
      2009 Annual Research Report
  • [Book] Number Theory : Drwmaing in dreams, Proc.5^<th> China-Japan Sem2009

    • Author(s)
      青木, 金光, Liu(共編
    • Total Pages
      252
    • Publisher
      World Scientific
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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