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Title:	Algorithms for chow-heegner points via iterated integrals
Author:	Darmon, Henri; Daub, Michael; Lichtenstein, Sam; Rotger Cerdà, Víctor
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres
Abstract:	Let E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on G0(N) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of so-called Chow-Heegner points, PT,f ¿ E(Q), indexed by algebraic correspondences T ¿ X0(N) × X0(N). It also gives an analytic formula, depending only on the image of T in cohomology under the complex cycle class map, for calculating PT,f numerically via Chen's theory of iterated integrals. The present work describes an algorithm based on this formula for computing the Chow-Heegner points to arbitrarily high complex accuracy, carries out the computation for all elliptic curves of rank 1 and conductor N < 100 when the cycles T arise from Hecke correspondences, and discusses several important variants of the basic construction.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Aritmètica -Mathematical ability -Aritmètica -Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Updated version Article
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