1996 Fiscal Year Final Research Report Summary
Estimates For Integer Points on Algebraic Variety by using Diophantine Approxiwatic
| Project/Area Number |
06640082
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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 | NIHON UNIVERSITY |
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Principal Investigator |
KOHNO Noriko NIHON UNIVERSITY,Department of Mathematics College of Science and Technology, Lecturer, 理工学部, 専任講師 (90215195)
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| Co-Investigator(Kenkyū-buntansha) |
SASAKI Ryuji NIHON UNIVERSITY,Department of Mathematics College of Science and Technology, Pr, 理工学部, 教授 (50120465)
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| Project Period (FY) |
1994 – 1996
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| Keywords | Diophantine Approximation / Diophantine equation / Elliptic Curve / Algebraic curve / Integer point / Transcendence / Transcendental Number / Transcendence Measure |
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| Research Abstract |
For transcendental number x, we consider Diophantine approximations by algebraic number beta in terms of height of beta and degree of beta. By using such approximation, called transcendental (or transcendence) measure, we observe integer points on algebraic curves, for example, elliptic curves. We obtain here a refinement for such measure when x comes from coordinates of inverse image by exponential map of rational points of an algebraic group defined over a number field, which is defined as a non trivial extention of a simple abelian variety by the additine group. We get also some finiteness result concerning with integer solutions to certain exponential Diophantine equations.
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