Bulletin of the Australian Mathematical Society

Research Article

On the size of integer solutions of elliptic equations

Yann Bugeauda1

a1 Université Louis Pasteur Mathématiques 7, rue René Descartes 67084 Strasbourg, Cedex France e-mail: bugeaud@math.u-strasbg.fr

Abstract

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.

(Received June 01 1997)