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Some consequences of Masser’s counting theorem on elliptic curves

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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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Acknowledgments

The authors would like to warmly thank Gaël Rémond as well as the referee for their precise reading and helpful comments on this article.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, UFC, 16 route de Gray, 25000, Besançon, France

    Aurélien Galateau

  2. EPFL, Station 8 - Bâtiment MA, CH-1015, Lausanne, Switzerland

    Valéry Mahé

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  1. Aurélien Galateau
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  2. Valéry Mahé
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Correspondence to Aurélien Galateau.

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Galateau, A., Mahé, V. Some consequences of Masser’s counting theorem on elliptic curves. Math. Z. 285, 613–629 (2017). https://doi.org/10.1007/s00209-016-1728-4

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  • DOI: https://doi.org/10.1007/s00209-016-1728-4

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