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Heegner Point Computations Via Numerical p-Adic Integration

  • Matthew Greenberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)

Abstract

Building on ideas of Pollack and Stevens, we present an efficient algorithm for integrating rigid analytic functions against measures obtained from automorphic forms on definite quaternion algebras. We then apply these methods, in conjunction with the Jacquet-Langlands correspondence and the Cerednik-Drinfeld theorem, to the computation of p-adic periods and Heegner points on elliptic curves defined over ℚ and \({\mathbb{Q}}(\sqrt{5})\) which are uniformized by Shimura curves.

Keywords

Modular Form Elliptic Curve Elliptic Curf Automorphic Form Quaternion Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthew Greenberg
    • 1
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontreal, QuebecCanada

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