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STUDIES ON D-MODULES DERIVED FROM CONFLUENT HYPERGEOMETRIC DIFFERENTIAL EQUATIONS

Research Project

Project/Area Number 09440052
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionOchanomizu University

Principal Investigator

MAJIMA Hideyuki  Ochanomizu University Dept. Math. Prof., 理学部, 教授 (50111456)

Co-Investigator(Kenkyū-buntansha) IWASAKI Katsunori  Kyushu University Dept. Math. Prof., 大学院・数理学研究科, 教授 (00176538)
ASAMOTO Nariko  Ochanomizu University, Dept. Inf. Sci. Assoc. Prof., 理学部, 助教授 (90222603)
YOSHIDA Hiroaki  Ochanomizu University, Dept. Inf. Sci. Assoc. Prof., 理学部, 助教授 (10220667)
TAKAYAMA Nobuki  Kobe University Dept. MAth. Prof., 理学部, 教授 (30188099)
KIMURA Hironobu  Kumamoto University Dept. Math. Prof., 理学部, 教授 (40161575)
三宅 正武  名古屋大学, 大学院・多元数理科学研究科, 教授 (70019496)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥7,100,000 (Direct Cost: ¥7,100,000)
Fiscal Year 1998: ¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 1997: ¥3,700,000 (Direct Cost: ¥3,700,000)
KeywordsConfluent hypergeometric function / Irregukar singular / Irregularity / Asymptotic expansion / Period relation / Intersection theory / Divergent solution / Airy function / 合流超幾何方程式 / D加群 / 不確定特異点
Research Abstract

1. Calculation of cohomology groups of solution complex of D-modules defined by confluent hypergeometric differential equations with values in the sheaves of germs of formal power-series ring and formal power-series ring with Gevrey order, by using projective resolutions of the D-modules similar to Koszul complex, which was invented by suggested information from 'KAN(a system' of computational algebraic analysis) made by Takayama
2. Asymptotic expansions of restrictions of generalized Airy functions by using relations between confluent hypergeometric functions with particular parameters and generalized Airy functions
3. Approximation formulas of coefficients of divergent solutions by using a vanishing theorem in asymptotic analysis in several variables
4. Constructionf of theory of intersection on the complex projective line for homology and cohomology groups defined by connections which are regular singular or not, and quadratic relations satisfied by confluent hypergeometric functions, as an analogue of period relations, by applying this theory.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] IWASAKI, Katsunori: "Asymptotic Analysis For Linear Difference Equations"Trans AMS. 349. 4107-4142 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] KIMURA, Hironobu: "On Rational de Rham Cohomology Associated with the Generalized Airy Function"Annali della Scoula Norm.Sup.di Pisa. 24. 351-366 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] MAJIMA, Hideyuki: "Some Isomorphism Theorems of Cohomology Groups for Completely integrable Connections"RIMS Kokyuroku. 1014. 31-35 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] MAJIMA, Hideyuki: "Irregularities on hypersurfaces of holonomic D-modules (especially definled by confluent hypergeometric partial differential equations)"RIMS Kokyuroku. 1090. 100-109 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 伊勢 康代: "合流超幾何微分方程式のストークス現象について"お茶の水女子大学大学院人間文化研究科数理情報科学専攻(修士論文). 51 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Iwasaki, Katsunori: "Asymptotic Analysis For Linear Difference Equations"Trans. AMS. Vol.349. 4107-4142 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kimura, Hironobu: "On Rational de Rham Cohomology associated with the Generalized Airy Function"Annali della Scoula Norm. Sup. di Pisa. Vol.24. 351-366 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] MAJIMA, Hdeyuki: "Some isomorphism theorems of cohomology groups for completely integrable connections"RIMS Kokyuroku. 1014. 31-35 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] MAJIMA, Hdeyuki: "Irregularties on hypersurfaces of holonomic D-modules (especially defined by confluent hypergeometric partial differential equations )"RIMS Kokyuroku. 1090. 100-109 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] ISE, Yasuyo: "On Stokes Phenomenun of Confluent Hypergeometric Diffrential Equations"Master Thesis, Math. and Computer Sci., Graduate School of Humanities and Sciences[Master's Program], Ochanomizu University. 51 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hideyuki MAJIMA: "Irreyularities on hypersurfaces of holononic D-modules (eapecially defined by confluent hypergeometric partial differntial equations)" RIMS Kokyuroku. 1090(4月刊行). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] IWASAKI, Katsunori: "Asymptotic Analysis for Linear difference Equations" Transactions of the American Mathematical Society. 349・10. 4107-4142 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] MAJIMA, Hideyuki: "Some isomorphsm the orems of cohomology groups for integrable"

    • Related Report
      1997 Annual Research Report
  • [Publications] "connecions" RIMS Kokyuroku. 1014. 31-35 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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