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arXiv:math/0305041 [math.NT]AbstractReferencesReviewsResources

A lower bound for the canonical height on elliptic curves over abelian extensions

Joseph H. Silverman

Published 2003-05-01Version 1

Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prove that there is a positive constant C(E/K) so that every nontorsion point P in E(K^ab) satisfies h(P) > C(E/K).

Journal: Journal of Number Theory 104 (2004), 353--372
Categories: math.NT, math.AC
Subjects: 11G05, 11G10, 14G25, 14K15
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