1997 Fiscal Year Final Research Report Summary
Algebraic and Analytic Research of Transcendental Numbers
| Project/Area Number |
08640056
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Gakushuin University |
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Principal Investigator |
IITAKA Shigeru Gakushuin Univ., Fucalty of Science Professor, 理学部, 教授 (20011588)
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| 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)
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| Project Period (FY) |
1996 – 1997
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| Keywords | Transcendental numbers / Algebraic independence / Diophantine equations / Functional equations |
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| 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.
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