Some consequences of Masser’s counting theorem on elliptic curves

Mathematische Zeitschrift, pp. 613-629, 2017.

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Keywords:
Line Bundle Elliptic Curve Elliptic Curf Abelian Variety Number Field

Abstract:

We use Masser’s counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser’s result with bounds on the rank and torsion of some groups of rational points on an elliptic curve.

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