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Algebraic and Analytic Research of Transcendental Numbers

Research Project

Project/Area Number 08640056
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

IITAKA Shigeru (1997)  Gakushuin Univ., Fucalty of Science Professor, 理学部, 教授 (20011588)

三井 孝美 (1996)  学習院大学, 理学部, 教授 (20080484)

Co-Investigator(Kenkyū-buntansha) NAKANO Shin  Gakushuin Univ., Fucalty of Science Associate Professor, 理学部, 助教授 (40180327)
MIZUTANI Akira  Gakushuin Univ., Fucalty of Science Professor, 理学部, 教授 (80011716)
KATASE Kiyoshi  Gakushuin Univ., Fucalty of Science Professor, 理学部, 教授 (70080489)
FUJIWARA Daisuke  Gakushuin Univ., Fucalty of Science Professor, 理学部, 教授 (10011561)
KURODA Shigetoshi  Gakushuin Univ., Fucalty of Science Professor, 理学部, 教授 (20011463)
飯高 茂  学習院大学, 理学部, 教授 (20011588)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1997: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1996: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsTranscendental numbers / Algebraic independence / Diophantine equations / Functional equations
Research Abstract

(a) In December 1996, "The 5-th Symposium of Transcendental Number Theory" was held at the main expense of this grant-in-aid. The fifteen research workers, including the three foreigners, delivered lectures on their new results concerning the transcendental number theory. For example,
i) New applications of the theory of Mahler functions,
ii) Exponential diophantine equations,
iii) A new attempt on the theory of Nesterenko,
iv) An extension of the theory of G-functions.
The proceedings of this symposium was published.
(b) We obtained new results on certain multiple series with "fractional powers" defined on an algebraic number field, which may be available for finding new transcendental numbers and deciding algebraic independence of special values. The multiple series is closely related to the zeta function on an algebraic number field with respect to Grossencharacter. By making use of this relation, we have proved the functional equation satisfied by the multiple series.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] T.Mitsui: "On certain multiple series with functional equation in a totally real number field II" Tokyo J.Math. 20. 299-313 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Mitsui: "On certain multiple series with functional equation in a totally imaginary number field II" (preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Mitsui: "On certain multiple series with transformation formula in an algebraic number field" (preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] D.Fujiwara and T.Tsuchida: "The time slicing approximation of the fundamental solution for the Schrodinger equation with electromagnetic fields" J.Math.Soc.Japan. 49. 299-327 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] D.Fujiwara, N.Kumano-go and K.Taniguchi: "A proof of estimates of Kumano-go-Taniguchi type for multiproduct of Fourier integral operators" Funkcial. Ekvac.40. 459-470 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] S.T.Kuroda and A.Mizutani: "Remarks on explicit numerical methods for Schrodinger equations" (in preparation).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] S.T.Kuroda and H.Nagatani: "H_<-2> construction and Hamiltonians with intersection of various type." RIMS Kokyuroku. 994. 155-167 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Mizutani and T.Suzuki: "On the iterative and minimizing sequences for semilinear elliptic equations (II)" J.Indust. Appl. Math.13. 351-367 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Mizutani and T.Suzuki: "Finite element approximation of degenerate parabolic equations" (in preparation).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 三井孝美: "On certain multiple series with functional equation in a totally real number field II" Tokyo J.Math.20. 299-313 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 藤原大輔: "The time slicing approximation of the fundamental solution for the Schrodinger equation with electromagnetic fields" J.Math.Soc.Japan. 49. 299-327 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 藤原大輔: "A proof of estimates of Kumano-go-Taniguchi type for multiproduct of Fourier integral operators" Funkcial.Ekvac.40. 459-470 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 黒田成俊・水谷明: "Remarks on explicit numerical methods for Schrodinger equations" (in preparation).

    • Related Report
      1997 Annual Research Report
  • [Publications] 三井孝美: "On certain multiple series with functional equation in a totally real number field II" Tokyo J.Math.(発表予定). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 藤原大輔: "The time slicing approximation of the fundamental solution for the Schrodinger equation with electromagnetic fields" J.Math.Soc.Japan. (発表予定). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 水谷明: "On the iterative and minimizing sequences for semilinear elliptic equations (II) (with T.Suzuki)" Japan J. Indust. Appl. Math.13. 351-367 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2021-09-27  

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