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2009 Fiscal Year Final Research Report

Research on Quasi-periodic continued fractions in terms of Special functions

Research Project

  • PDF
Project/Area Number 18540006
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KOMATSU Takao  Hirosaki University, 大学院・理工学研究科, 教授 (70300556)

Research Collaborator SHIOKAWA Iekata  慶応大学, 理工学部, 名誉教授
BOWMAN Dougalas  北イリノイ大学, 数理科学科, 教授(合衆国)
ELSNER Carsten  ハノーヴァー応用科学大学, 教授(ドイツ)
LAOHAKOSOL Vichian  カセットサート大学, 数学科, 教授(タイ)
CALDWELL Chris  テネシー大学, マーチン校・数学統計学科, 教授(合衆国)
Project Period (FY) 2006 – 2009
Keywords整数論 / 関数論 / 組合せ論 / 代数学
Research Abstract

Still new types of Hurwitz and Tasoev continued fractions, which belong to quasi-periodic continued fractions, have been found. Several typical relations between quasi-periodic continued fractions and hypergeometric functions, hyperbolic functions, Fibonacci-zeta functions have been discovered. Leaping convergents have been defined from the concept of convergents of quasi-periodic continued fractions. Characteristic properties of leaping convergents have been examined. Leaping convergents have been extensively defined on non-regular continued fractions and on general integer sequences.

  • Research Products

    (13 results)

All 2009 2008 2007 2006

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (3 results) Book (4 results)

  • [Journal Article] On convergents formed from Diophantine equations2009

    • Author(s)
      Carsten Elsner, Takao Komatsu, Iekata Shiokawa
    • Journal Title

      Glasnik Mat. 44

      Pages: 267-284

    • Peer Reviewed
  • [Journal Article] Shrinking the period length of quasi-periodic continued fractions2009

    • Author(s)
      Takao Komatsu
    • Journal Title

      J. Number Theory 129

      Pages: 358-366

    • Peer Reviewed
  • [Journal Article] On the residue classes of integer sequences satisfying a linear three-term recurrence formula2008

    • Author(s)
      Carsten Elsner, Takao Komatsu
    • Journal Title

      Linear Algebra Appl. 429

      Pages: 993-947

    • Peer Reviewed
  • [Journal Article] Approximation of values of hyperbolic functions by restricted rationals2007

    • Author(s)
      Carsten Elsner, Takao Komatsu, Iekata Shiokawa
    • Journal Title

      J. Theorie des Nombres de Bordeaux 19

      Pages: 393-404

    • Peer Reviewed
  • [Journal Article] Hurwitz continued fractions with confluent hypergeometric functions2007

    • Author(s)
      Takao Komatsu
    • Journal Title

      Czech. Math. J. 57

      Pages: 919-932

    • Peer Reviewed
  • [Journal Article] Continued fraction of e^2 with confluent hypergeometric functions2006

    • Author(s)
      Takao Komatsu
    • Journal Title

      Liet. Mat. Rink. 46

      Pages: 513-531

    • Peer Reviewed
  • [Presentation] Arithmetical properties of Fibonacci Zeta functions2009

    • Author(s)
      Takao Komatsu
    • Organizer
      JA2009
    • Place of Presentation
      サンテティエンヌ大学 フランス
    • Year and Date
      20090706-20090710
  • [Presentation] Three term recurrence relations and continued fractions2008

    • Author(s)
      Takao Komatsu
    • Organizer
      4th Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      POSTECH 浦項 韓国
    • Year and Date
      20080201-20080202
  • [Presentation] Some combinatorial properties of leaping convergents, II2006

    • Author(s)
      Takao Komatsu
    • Organizer
      12th International Conference on Fibonacci numbers and their applications
    • Place of Presentation
      サンフランシスコ州立大学 合衆国
    • Year and Date
      20060717-20060721
  • [Book] 解析的整数論の新しい展開2009

    • Author(s)
      Takao Komatsu
    • Total Pages
      186
    • Publisher
      京都大学数理解析研究所講究録
  • [Book] Advances in Mathematics Research2009

    • Author(s)
      Takao Komatsu, 他11名
    • Total Pages
      345
    • Publisher
      Nova Publishers
  • [Book] Diophantine Analysis and Related Fields-DARF 2007/20082008

    • Author(s)
      Takao Komatsu
    • Total Pages
      211
    • Publisher
      American Institute of Physics
  • [Book] Diophantine Analysis and Related Fields 2006(Seminar on Mathematical Sciences No. 35)2006

    • Author(s)
      Masanori Katsurada, Takao Komatsu, Hitoshi Nakada
    • Total Pages
      221
    • Publisher
      Keio University

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Published: 2011-06-18   Modified: 2016-04-21  

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