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Analytic, Algebraic and Combinatorial studies on continued fractions

Research Project

Project/Area Number 22540005
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  弘前大学, 理工学研究科, 教授 (70300556)

Co-Investigator(Renkei-kenkyūsha) MUNEMASA Akihiro  東北大学, 大学院情報科学研究科, 教授 (50219862)
AKIYAMA Shigeki  筑波大学, 大学院数理物質科学研究科, 教授 (60212445)
TANAKA Takaaki  慶応義塾大学, 理工学部, 講師 (60306850)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords数論 / 代数学 / 組み合わせ論 / 連分数 / 整数論 / 組合せ論 / 線形関係式 / Leaping convergents
Research Abstract

Analytic studies of continued fractions are to obtain exact algebraic expressions for approximation evalucations of various Hurwitz and Tasoev continued fractions, some relations between Fibonacci-zeta functions and continued fractions, and some relations between zeta functions and Cauchy polynomials. Algebraic studies of continued fractions are to obtain independence measures of arithmetic functions and to construct Liouville numbers in non- Archimedean case. Combinatorial studies of continued fractions are to give upper bounds on cyclotomic numbers, and to discover linear recurrence relations associated with multinomial Pascal triangles. In addition, cross-studies of continued fractions are to show some relations among continued fractions, Fibonacci numbers and congruent numbers, and to discover the concept of poly Cauchy numbers and polynomials as some generalizations of Cauchy numbers, which are related with Bernoulli numbers.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (78 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (41 results) (of which Peer Reviewed: 35 results) Presentation (35 results) (of which Invited: 8 results) Book (1 results) Remarks (1 results)

  • [Journal Article] A generalization of poly-Cauchy numbers and their properties2013

    • Author(s)
      Takao Komatsu, V. Laohakosol and K. Liptai
    • Journal Title

      Abstract Appl. Anal.

      Volume: Article ID 179841 Pages: 8-8

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Poly-Cauchy polynomials2013

    • Author(s)
      Takao Komatsu and K. Kamano
    • Journal Title

      Mosc. J. Comb. Number Theory

      Volume: 3 Pages: 181-207

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On convergents of certain values of hyperbolic functions formed from Diophantine equations2013

    • Author(s)
      T. Chaichana, Takao Komatsu and V. Laohakosol
    • Journal Title

      Tokyo J. Math.

      Volume: 36 Pages: 239-251

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the distance between products of consecutive Fibonacci numbers and powers of Fibonacci numbers2013

    • Author(s)
      J. J. Bravo, Takao Komatsu and F. Luca
    • Journal Title

      Indag. Math.

      Volume: 24 Pages: 181-198

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hypergeometric Cauchy numbers2013

    • Author(s)
      Takao Komatsu
    • Journal Title

      Int. J. Number Theory

      Volume: 9 Pages: 545-560

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Poly-Cauchy numbers with a q parameter2013

    • Author(s)
      Takao Komatsu
    • Journal Title

      Ramanujan J.

      Volume: 31 Pages: 353-371

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Upper bounds on cyclotomic numbers2013

    • Author(s)
      K. Betsumiya, M. Hirasaka, Takao Komatsu and A. Munemasa
    • Journal Title

      Linear Algebra Appl.

      Volume: 438 Pages: 111-120

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Poly-Cauchy numbers2013

    • Author(s)
      Takao Komatsu
    • Journal Title

      Kyushu. J. Math.

      Volume: 67 Pages: 143-153

    • NAID

      130003364805

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sums of products of Cauchy numbers, including poly-Cauchy numbers2013

    • Author(s)
      Takao Komastsu
    • Journal Title

      J. Discrete Math.

      Volume: 2013

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers2013

    • Author(s)
      Takao Komatsu and F. Luca
    • Journal Title

      Ann. Math. Inform.

      Volume: 41 Pages: 99-105

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Poly-Cauchy polynomials2013

    • Author(s)
      K. Kamano and Takao Komatsu
    • Journal Title

      Mosc. J. Comb. Number Theory

      Volume: 3

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Poly-Cauchy polynomials2013

    • Author(s)
      Takao Komatsu
    • Journal Title

      8eme Recontre d’Analyse Mathematique et ses Applications (RAMA8) Resumes/Abstracts, Alger, 26―29 Novembre 2012, Faculte de Mathematiques, USTHB

      Volume: なし Pages: 14-14

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Some exact algebraic expressions for the tails of Tasoev continued fractions2012

    • Author(s)
      Takao Komatsu
    • Journal Title

      J. Austral. Math. Soc.

      Volume: 92 Pages: 179-193

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Independence measures of arithmetic functions II2012

    • Author(s)
      Takao Komatsu, V. Laohakosol and P. Ruengsinsub
    • Journal Title

      Acta Arith.

      Volume: 153 Pages: 199-216

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Congruent numbers and continued fractions2012

    • Author(s)
      T. Komatsu
    • Journal Title

      Fibonacci Quarterly

      Volume: 50 Pages: 222-226

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear recurrence relations associated with multinomial Pascal triangles2012

    • Author(s)
      T. Komatsu
    • Journal Title

      Math. Pannon

      Volume: 23 Pages: 135-146

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear recurrence relations associated with multinomial Pascal triangles, II2012

    • Author(s)
      T. Komatsu
    • Journal Title

      Far East J. Math. Sci.

      Volume: 67 Pages: 153-180

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On convergents of certain values of Tasoev continued fractions associated with Diophantine equations2012

    • Author(s)
      T. Komatsu
    • Journal Title

      Mat. Metodi Fiz.-Mekh. Polya

      Volume: 55 Pages: 16-22

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some relationships between poly-Cauchy type numbers and poly-Bernoulli type numbers2012

    • Author(s)
      T. Komatsu, K. Liptai and L. Szalay
    • Journal Title

      East-West J. Math.

      Volume: 14 Pages: 114-120

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the multiplicative order of F_{n+1}/F_n modulo F_m2012

    • Author(s)
      T. Komatsu, F. Luca and Y. Tachiya
    • Journal Title

      Integers

      Volume: 12B

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Poly-Cauchy numbers2012

    • Author(s)
      T. Komatsu
    • Journal Title

      数理解析研究所講究録

      Volume: 1806 Pages: 42-53

    • NAID

      130003364805

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Results about dependence and convolution2012

    • Author(s)
      T. Komatsu, P. Ruengsinsub, V. Laohakosol and S. Srisopha
    • Journal Title

      数理解析研究所講究録

      Volume: 1806 Pages: 54-64

    • Related Report
      2012 Annual Research Report
  • [Journal Article] On the sum of reciprocal generalized Fibonacci numbers2011

    • Author(s)
      S. H. Holliday and Takao Komatsu
    • Journal Title

      INTEGERS

      Volume: 11 Pages: 441-455

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Independence measures of arithmetic functions2011

    • Author(s)
      Takao Komatsu, V. Laohakosol and P. Ruengsinsub
    • Journal Title

      J. Number Theory

      Volume: 131 Pages: 1-17

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the sum of reciprocal generalized Fibonacci numbers2011

    • Author(s)
      T. Komatsu and S. H. Holliday
    • Journal Title

      Integers

      Volume: 11 Pages: 441-455

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the sum of reciprocal Tribonacci numbers2011

    • Author(s)
      T. Komatsu
    • Journal Title

      Ars Combin.

      Volume: 98 Pages: 447-459

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the nearest integer of the sum of the reciprocal Fibonacci numbers2011

    • Author(s)
      T. Komatsu
    • Journal Title

      Aportaciones Matematicas Investigacion

      Volume: 20 Pages: 171-184

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Leaping convergents of Hurwitz continued fractions2011

    • Author(s)
      T. Komatsu
    • Journal Title

      Discuss. Math. Gen. Algebra Appl.

      Volume: 31 Pages: 101-121

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Leaping convergents of Tasoev continued fractions2011

    • Author(s)
      T. Komatsu
    • Journal Title

      Discuss. Math. Gen. Algebra Appl.

      Volume: 31 Pages: 201-216

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Powers of Sierpinski numbers base b2010

    • Author(s)
      C. K. Caldwell and Takao Komatsu
    • Journal Title

      INTEGERS

      Volume: 10 Pages: 423-436

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Liouville numbers in non-Archimedean situation2010

    • Author(s)
      T. Chaichana, Takao Komatsu and V. Laohakosol
    • Journal Title

      Publ. Math. Debrecen

      Volume: 77 Pages: 39-63

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some periodicities in the continued fraction expansions of Fibonacci and Lucas Dirichlet series2010

    • Author(s)
      Chris K.Caldwell, Takao Komatsu
    • Journal Title

      Fibonacci Quarterly

      Volume: 48 Pages: 47-55

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Liouville numbers in non-Archimedean situation2010

    • Author(s)
      Tuangrat Chaichana, Takao Komatsu, Vichian Laohakosol
    • Journal Title

      Publicationes Mathematicae Debrecen

      Volume: 77 Pages: 39-63

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some combinatorial properties of the leaping convergents, II2010

    • Author(s)
      Takao Komatsu
    • Journal Title

      Cogressus Numerantium

      Volume: 2000 Pages: 187-196

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the sum of reciprocal numbers satisfying a recurrence relations of orders2010

    • Author(s)
      Takao Komatsu, Vichian Laohakosol
    • Journal Title

      Journal of Integer Sequences

      Volume: 13

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Four-term leaping recurrence relations2010

    • Author(s)
      Takao Komatsu
    • Journal Title

      Linear and Multilinear Algebra

      Volume: 58 Pages: 875-886

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Powers of Sierpinski numbers base b2010

    • Author(s)
      Chris K.Caldwell, Takao Komatsu
    • Journal Title

      Integers

      Volume: 10 Pages: 423-436

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sequences Hn for which Hn/Hn+1 approaches an irrational number2010

    • Author(s)
      Takao Komatsu
    • Journal Title

      Fibonacci Quarterly

      Volume: 48 Pages: 265-275

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some recognizable forms of simple continued fractions2010

    • Author(s)
      Takao Komatsu
    • Journal Title

      AIP conference proceedings

      Volume: 1264 Pages: 27-40

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Characterization of linear recurrences associated to rays in Pascal's triangle2010

    • Author(s)
      Hacene Belbachir, Takao Komatsu, Laszlo Szalay
    • Journal Title

      AIP Conference Proceedings

      Volume: Vol.1264

    • Related Report
      2010 Annual Research Report
  • [Journal Article] パスカルの三角形から生じる線形関係列2010

    • Author(s)
      小松尚夫
    • Journal Title

      日本数学会代数学分科会講演アブストラクト

      Pages: 62-63

    • Related Report
      2010 Annual Research Report
  • [Presentation] $a$-, $q$-, $¥lambda$- generalization of poly-Bernoulli numbers and poly-Cauchy numbers2014

    • Author(s)
      Takao Komatsu
    • Organizer
      Korean–Japan Workshop on Algebra and Combinatorics 2014 (KJ2014)
    • Place of Presentation
      KAIST、韓国
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Convolution identities for Cauchy numbers2013

    • Author(s)
      Takao Komatsu
    • Organizer
      Integers Conference
    • Place of Presentation
      University of West Georgia, USA
    • Related Report
      2013 Final Research Report
  • [Presentation] Some remarks on poly-Cauchy numbers and polynomials2013

    • Author(s)
      Takao Komatsu
    • Organizer
      JA2013
    • Place of Presentation
      フーリエ研究所、グルノーブル、フランス
    • Related Report
      2013 Final Research Report
  • [Presentation] Poly-Cauchy numbers and their combinatorial properties2013

    • Author(s)
      Takao Komatsu
    • Organizer
      The 13th Japan-Korea Workshop on Algebra and Combinatorics
    • Place of Presentation
      九州大学
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] Some remarks on the poly-Cauchy numbers and polynomials2013

    • Author(s)
      Takao Komatsu
    • Organizer
      JA2013
    • Place of Presentation
      フーリエ研究所、グルノーブル、フランス
    • Related Report
      2013 Annual Research Report
  • [Presentation] 多重ベルヌーイ多項式を含むベルヌーイ多項式の積和公式2013

    • Author(s)
      小松 尚夫
    • Organizer
      第8回福岡数論研究集会
    • Place of Presentation
      九州大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Covolution identities for Cauchy numbers2013

    • Author(s)
      Takao Komatsu
    • Organizer
      Integers Conference
    • Place of Presentation
      University of West Georgia, USA
    • Related Report
      2013 Annual Research Report
  • [Presentation] Covolution identities for Cauchy numbers2013

    • Author(s)
      Takao Komatsu
    • Organizer
      解析的整数論研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] Balancing with binomial coefficients2013

    • Author(s)
      Takao Komatsu
    • Organizer
      第10回「代数学と計算」研究集会 (AC2013)
    • Place of Presentation
      首都大学東京
    • Related Report
      2013 Annual Research Report
  • [Presentation] Sums of products of Cauchy numbers, including generalized poly-Cauchy numbers2013

    • Author(s)
      T. Komatsu
    • Organizer
      Diophantine Analysis and related fields 2013
    • Place of Presentation
      日本大学理工学部
    • Related Report
      2012 Annual Research Report
  • [Presentation] Poly-Cauchy polynomials2013

    • Author(s)
      K. Kamano and T. Komatsu
    • Organizer
      日本数学会年会代数学分科会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Poly-Cauchy polynomials2012

    • Author(s)
      Takao Komatsu
    • Organizer
      RAMA8(8eme Rencontre d'Analyse Mathematique et ses Applications)
    • Place of Presentation
      USTHB アルジェ(アルジェリア)
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Poly-Cauchy numbers and their characteristic properties2012

    • Author(s)
      Takao Komatsu
    • Organizer
      ICNA2012 (International conference in Number Theory and applications 2012)
    • Place of Presentation
      カセットサート大学タイ王国
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers2012

    • Author(s)
      Takao Komatsu
    • Organizer
      The 15th International Conference on Fibonacci numbers and their applications
    • Place of Presentation
      エステルハーズィ・カーロィ教育大学 エゲル ハンガリー
    • Related Report
      2013 Final Research Report
  • [Presentation] Hypergeometric Cauchy numbers2012

    • Author(s)
      Takao Komatsu
    • Organizer
      数系と置換2012
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers2012

    • Author(s)
      T. Komatsu
    • Organizer
      The 15th International Conference on Fibonacci numbers and their applications
    • Place of Presentation
      ハンガリー エステルハーズィ・カーロィ教育大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Poly-Cauchy numbers and their characteristic properties2012

    • Author(s)
      T. Komatsu
    • Organizer
      International conference in Number Theory and applications 2012
    • Place of Presentation
      タイ カセットサート大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Cauchy numbers and Bernoulli numbers2012

    • Author(s)
      T. Komatsu
    • Organizer
      解析的整数論研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] Poly-Cauchy polynomials2012

    • Author(s)
      T. Komatsu
    • Organizer
      8eme Rencontre d’Analyse Mathematique et ses Applications
    • Place of Presentation
      アルジェリア USTHB
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Poly-Cauchy numbers and Riordan Arrays2012

    • Author(s)
      T. Komatsu
    • Organizer
      Diophantine Analysis and related fields 2012
    • Place of Presentation
      新潟大学「ときめいと」キャンパス
    • Related Report
      2011 Annual Research Report
  • [Presentation] On poly-Cauchy numbers2012

    • Author(s)
      T. Komatsu
    • Organizer
      The 12th Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      韓国 POSTECH
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] On poly-Cauchy numbers and polynomials2012

    • Author(s)
      T. Komatsu
    • Organizer
      International Number Theory Conference in memory of Alf van der Poorten, AM
    • Place of Presentation
      オーストラリア Noah's on the beach, Newcastle
    • Related Report
      2011 Annual Research Report
  • [Presentation] On some characteristic properties of linear recurrence relations associated to rays in Pascal's triangle and combinatorial identities2011

    • Author(s)
      Takao Komatsu
    • Organizer
      The 3rd Science Research Conference
    • Place of Presentation
      タィ・Naresuan大学
    • Year and Date
      2011-03-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Hurwitz連分数, Tasoev連分数と¥¥ディオファントス近似2011

    • Author(s)
      小松尚夫
    • Organizer
      日本数学会東北支部会
    • Place of Presentation
      東北大学川井ホール(特別講演)
    • Year and Date
      2011-02-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Hurwitz連分数,Tasoev連分数とディオファントス近似2011

    • Author(s)
      小松尚夫
    • Organizer
      日本数学会東北支部会総会
    • Place of Presentation
      東北大学川井ホール
    • Year and Date
      2011-02-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Characterization of linear recurrence sequences associated to rays in Pascal's triangle and combinatorial identities2011

    • Author(s)
      Takao Komatsu
    • Organizer
      The 9th Japan-Korea Workshop on Algebra and Combinatorics
    • Place of Presentation
      東北大学情報科学研究科
    • Year and Date
      2011-01-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Diophantine approximations of Hurwitz and Tasoev continued fractions2011

    • Author(s)
      Takao Komatsu
    • Organizer
      International Skorobohat'ko Mathematical Conference
    • Place of Presentation
      Ivan Franko Pedagogical University of Drohobych, Drohobych, ウクライナ
    • Related Report
      2013 Final Research Report
  • [Presentation] Three-term leaping recurrence relations and their extensions2011

    • Author(s)
      Takao Komatsu
    • Organizer
      DIMACOS11-FSTM, International Conference on Discrete Mathematics & Computer Sciences
    • Place of Presentation
      ハッサン第2大学、モハメディア、モロッコ
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Leaping convergents of Tasoev continued fractions2011

    • Author(s)
      T. Komatsu
    • Organizer
      DIMACOS11-FSTM, International Conference on Discrete Mathematics & Computer Sciences
    • Place of Presentation
      モロッコ ハッサン第2大学
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Diophantine approximations of Hurwitz and Tasoev continued fractions2011

    • Author(s)
      T. Komatsu
    • Organizer
      International Skorobohat'ko Mathematical Conference
    • Place of Presentation
      ウクライナ Ivan Franko Pedagogical University of Drohobych
    • Related Report
      2011 Annual Research Report
  • [Presentation] Poly-Cauchy numbers2011

    • Author(s)
      T. Komatsu
    • Organizer
      解析的整数論研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Annual Research Report
  • [Presentation] Arithmetical properties of the leaping convergents of continued fractions2010

    • Author(s)
      Takao Komatsu
    • Organizer
      解析的整数論研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] パスカルの三角形から生じる線形関係列2010

    • Author(s)
      小松尚夫
    • Organizer
      日本数学会秋季総合分科会代数学分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the nearest integer of the sum of the reciprocal Fibonacci numbers2010

    • Author(s)
      Takao Komatsu
    • Organizer
      The 14th International Conference on Fibonacci numbers and their applications
    • Place of Presentation
      メキシコ・モレリア数学研究所
    • Year and Date
      2010-07-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the nearest integer of the sum of reciprocal Fibonacci numbers2010

    • Author(s)
      Takao Komatsu
    • Organizer
      The 14th International Conference on Fibonacci numbers and their applications
    • Place of Presentation
      メキシコ国立自治大学モレリア数学研究所
    • Related Report
      2013 Final Research Report
  • [Book] AIP conference proceedings 12642010

    • Author(s)
      Takao Komatsu
    • Total Pages
      151
    • Publisher
      American Institute of Physics
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.st.hirosaki-u.ac.jp/~komatsu/kenkyu.html

    • Related Report
      2013 Final Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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