Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Details Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

2012-03-17

arxiv.org/abs/1203.3865v1

Mathematics

Number Theory

31 pages

Scientific paper

We establish new upper bounds for the height of the S-integral points of an elliptic curve. The proof uses the elliptic analogue of Baker's method, based on lower bounds for linear forms in elliptic logarithms. We then prove that the conjecture of B. J. Birch and H. P. F. Swinnerton-Dyer for a single elliptic curve over number fields would imply a result in the direction of the abc-conjecture over number fields.

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