dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres
dc.contributor.author
Darmon, Henri
dc.contributor.author
Daub, Michael
dc.contributor.author
Lichtenstein, Sam
dc.contributor.author
Rotger Cerdà, Víctor
dc.identifier
Darmon, H., Daub, M., Lichtenstein, S., Rotger, V. Algorithms for chow-heegner points via iterated integrals. "Mathematics of computation", 2015, vol. 84, núm. 295, p. 2505-2547.
dc.identifier
https://hdl.handle.net/2117/78758
dc.description.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.
dc.description.abstract
Peer Reviewed
dc.description.abstract
Postprint (updated version)
dc.format
application/pdf
dc.rights
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights
Restricted access - publisher's policy
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Aritmètica
dc.subject
Mathematical ability
dc.subject
Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry
dc.title
Algorithms for chow-heegner points via iterated integrals
