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 \mathbbQ(Ö5){\mathbb{Q}}(\sqrt{5}) which are uniformized by Shimura curves.
Heegner points, p-adic L-functions, and the Cerednik-Drinfeld uniformization / M. Bertolini, H. Darmon. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 131:3(1998), pp. 453-491. [10.1007/s002220050211]
Heegner points, p-adic L-functions, and the Cerednik-Drinfeld uniformization
M. Bertolini;
1998
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 \mathbbQ(Ö5){\mathbb{Q}}(\sqrt{5}) which are uniformized by Shimura curves.
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