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.
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Greenberg, M. (2006). Heegner Point Computations Via Numerical p-Adic Integration. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_26
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DOI: https://doi.org/10.1007/11792086_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36075-9
Online ISBN: 978-3-540-36076-6
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