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Efficient calculation of Stark-Heegner points via overconvergent modular symbols

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Abstract

This note presents a qualitative improvement to the algorithm presented in [DG] for computing Stark-Heegner points attached to an elliptic curve and a real quadratic field. This algorithm computes the Stark-Heegner point with ap-adic accuracy ofM significant digits in time which is polynomial inM, the primep being treated as a constant, rather than theO(p M) operations required for the more naive approach taken in [DG]. The key to this improvement lies in the theory of overconvergent modular symbols developed in [PS1] and [PS2].

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Authors and Affiliations

  1. Department of Mathematics, McGill University, Burnside Hall 805 Sherbrooke Street West, H3A 2K6, Montreal, QC, Canada

    Henri Darmon

  2. Department of Mathematics, Boston University, 02215, Boston, MA, USA

    Robert Pollack

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  1. Henri Darmon
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  2. Robert Pollack
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Correspondence to Henri Darmon.

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Darmon, H., Pollack, R. Efficient calculation of Stark-Heegner points via overconvergent modular symbols. Isr. J. Math. 153, 319–354 (2006). https://doi.org/10.1007/BF02771789

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  • DOI: https://doi.org/10.1007/BF02771789

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