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On the size of integer solutions of elliptic equations

Published online by Cambridge University Press:  17 April 2009

Yann Bugeaud
Yann Bugeaud
Affiliation:
Université Louis PasteurMathématiques7, rue René Descartes67084 Strasbourg, CedexFrance e-mail: [email protected]
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Abstract

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We improve upon earlier effective bounds for the magnitude of integer points on an elliptic curve ε defined over a number field K. We slightly refine the dependence on the discriminant of K. In most of the previous papers, the estimates obtained are exponential in the height of ε. In this work, taking also into consideration the prime ideals dividing the discriminant of ε, we provide a totally explicit bound which is only polynomial in the height.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 199 - 206
Copyright
Copyright © Australian Mathematical Society 1998

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