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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Prime power terms in elliptic divisibility sequences
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by Valéry Mahé PDF
Math. Comp. 83 (2014), 1951-1991 Request permission

Abstract:

We study a problem on specializations of multiples of rational points on elliptic curves analogous to the Mersenne problem. We solve this problem when descent via isogeny is possible by giving explicit bounds on the indices of prime power terms in elliptic divisibility sequences associated to points in the image of a nontrivial isogeny. We also discuss the uniformity of these bounds assuming the Hall–Lang conjecture.
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Additional Information
  • Valéry Mahé
  • Affiliation: École Polytechnique Fédérale de Lausanne, SB-IMB-CSAG, Station 8, CH-1015 Lausanne, Switzerland.
  • Email: valery.mahe@epfl.ch
  • Received by editor(s): December 24, 2009
  • Received by editor(s) in revised form: October 15, 2011, and October 31, 2012
  • Published electronically: November 12, 2013
  • Additional Notes: This work was supported by EPSRC grant EP/E012590/1, the Université de Montpellier 2, the Université de Franche-Comté and the École Polytechnique Fédérale de Lausanne. The author thanks Professor Everest, Professor Silverman, Professor Stevens and the anonymous referee for helpful discussions and comments.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 1951-1991
  • MSC (2010): Primary 11G05, 11A41
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02790-1
  • MathSciNet review: 3194137