• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

A Research on the Theory of Irrational Numbers for q-Functions

Research Project

Project/Area Number 15540006
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

AMOU Masaaki  Gunma University, Faculty of Engineering, Professor, 工学部, 助教授 (60201901)

Co-Investigator(Kenkyū-buntansha) SAITOU Saburho  Gunma University, Faculty of Engineering, Professor, 工学部, 教授 (10110397)
IKEHATA Masaru  Gunma University, Faculty of Engineering, Professor, 工学部, 教授 (90202910)
AMANO Kazuo  Gunma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (90137795)
TANUMA Kazumi  Gunma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60217156)
KATSURADA Masanori  Keio University, Faculty of Economics, Professor, 経済学部, 教授 (90224485)
佐藤 久  群馬大学, 工学部, 助手 (60008513)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsq-Function / q-Difference Equation / Irrational Number / Linear Independence / Shidlovskii's Lemma
Research Abstract

We have obtained the following results mainly on the theory of irrational numbers for q-functions.
1. We estimated from above the dimension of the vector space generated by certain special values of functions satisfying linear q-difference equations with polynomial coefficients. The head investigator submitted a paper on the result with Prof.Matala-aho (University of Oulu).
2. We proved a complete analogue of Shidlovskii's lemma, both on Pade-type approximations of the first and the second kinds, for a system of q-difference equations with coefficients from rational functions. Moreover, we apply this result to get linear independence of special values of analytic functions satisfying the above system. The head investigator is preparing a paper on the result with Prof.Vaananen (University of Oulu, a investigator from abroad) and Prof.Matala-aho.
3. We convined a criterion on linear independence of functions given by Galochkin with an inductive method in Mahler functions given by Duverney-Nishioka, and created a method to obtaining a quantitative refinement of a resul of Duverney-Nishioka. The head investigator is preparing a paper on the result with Prof.Vaananen.
By the support of the grant concerned, the head investigator visited Belarus (August, 2003) and Finland (September, 2003 ; September-October, 2005), and invited Prof.Kohnen and Prof.Lasjaunias (October, 2004), which were very important for the present research.

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report

Research Products

(14 results)

All 2005 2004 Other

All Journal Article (12 results) Publications (2 results)

  • [Journal Article] Linear independence of the values of q-hypergeometric series and related functions.2005

    • Author(s)
      Masaaki Amou, Keijo Vaananen
    • Journal Title

      The Ramanujan J. 9

      Pages: 317-339

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On linear independence of the theta values.2005

    • Author(s)
      Masaaki Amou, Keijo Vaananen
    • Journal Title

      Monasch. Math. 144

      Pages: 1-11

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Sur la separation des racines des polynomes et une question de Sprindzuk.2005

    • Author(s)
      Masaaki Amou, Yann Bugeaud
    • Journal Title

      The Ramanujan J. 9

      Pages: 25-32

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Linear independence of the values of q-hypergeometric series and related functions2005

    • Author(s)
      M.Amou, K.Vaananen
    • Journal Title

      The Ramanujan J. 9

      Pages: 317-339

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On linear independence of the theta values2005

    • Author(s)
      M.Amou, K.Vaananen
    • Journal Title

      Monasch.Math. 144

      Pages: 1-11

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Sur la separation des racines des polynomes et une question de Sprindzuk2005

    • Author(s)
      M.Amou, Y.Bugeaud
    • Journal Title

      The Ramanujan J. 9

      Pages: 25-32

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Linear independence of the values of q-hypergeometric series and related functions2005

    • Author(s)
      M.Amou, K.Vaananen
    • Journal Title

      Ramanujan J. 9巻

      Pages: 317-339

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Sur la separation des racines des polynomes et une question de Sprindzuk2005

    • Author(s)
      M.Amou, Y.Bugeaud
    • Journal Title

      Ramanujan J. 9巻

      Pages: 25-32

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On linear independence of the theta values2005

    • Author(s)
      M.Amou, K.Vaananen
    • Journal Title

      Manasch.Math. 144巻

      Pages: 1-11

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Sur la separation des racines des polynomes et une question de Sprindzuk2005

    • Author(s)
      M.Amou, Y.Bugeaud
    • Journal Title

      Ramanujan J. 9巻(in press)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Irrationality results for values of generalized Tcshakaloff series II.2004

    • Author(s)
      Masaaki Amou, Masanori Katsurada
    • Journal Title

      J. Number Theory 104

      Pages: 132-155

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Irrationality results for values of generalized Tschakaloff series II2004

    • Author(s)
      M.Amou, M.Katsurada
    • Journal Title

      J. Number Theory 104

      Pages: 132-155

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] M.Amou, K.Vaananen: "An analogue of Shidlovskii's lemma for certain q-difference equations"Aequationes Math.. 65巻. 93-101 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Amou, M.Katsurada: "Irrationality results for values of generalized Tschkaloff series II"J.Number Theory. 104巻1号. 132-155 (2004)

    • Related Report
      2003 Annual Research Report

URL: 

Published: 2003-03-31   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi