Heegner points on Cartan non-split curves

Let E/ℚ be an elliptic curve of conductor N, and let K be an imaginary quadratic field such that the root number of E/K is -1. Let O be an order in K and assume that there exists an odd prime p such that p2 ∥ N, and p is inert in O. Although there are no Heegner points on X0(N) attached to O, in thi...

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Detalles Bibliográficos
Autor principal: Pacetti, Ariel Martin
Publicado: 2016
Materias:
Cartan curves
Heegner points
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0008414X_v68_n2_p422_Kohen
http://hdl.handle.net/20.500.12110/paper_0008414X_v68_n2_p422_Kohen
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0008414X_v68_n2_p422_Kohen
record_format dspace
spelling paper:paper_0008414X_v68_n2_p422_Kohen2023-06-08T14:31:59Z Heegner points on Cartan non-split curves Pacetti, Ariel Martin Cartan curves Heegner points Let E/ℚ be an elliptic curve of conductor N, and let K be an imaginary quadratic field such that the root number of E/K is -1. Let O be an order in K and assume that there exists an odd prime p such that p2 ∥ N, and p is inert in O. Although there are no Heegner points on X0(N) attached to O, in this article we construct such points on Cartan non-split curves. In order to do that, we give a method to compute Fourier expansions for forms on Cartan non-split curves, and prove that the constructed points form a Heegner system as in the classical case. © Canadian Mathematical Society 2016. Fil:Pacetti, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0008414X_v68_n2_p422_Kohen http://hdl.handle.net/20.500.12110/paper_0008414X_v68_n2_p422_Kohen
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cartan curves
Heegner points
spellingShingle Cartan curves
Heegner points
Pacetti, Ariel Martin
Heegner points on Cartan non-split curves
topic_facet Cartan curves
Heegner points
description Let E/ℚ be an elliptic curve of conductor N, and let K be an imaginary quadratic field such that the root number of E/K is -1. Let O be an order in K and assume that there exists an odd prime p such that p2 ∥ N, and p is inert in O. Although there are no Heegner points on X0(N) attached to O, in this article we construct such points on Cartan non-split curves. In order to do that, we give a method to compute Fourier expansions for forms on Cartan non-split curves, and prove that the constructed points form a Heegner system as in the classical case. © Canadian Mathematical Society 2016.
author Pacetti, Ariel Martin
author_facet Pacetti, Ariel Martin
author_sort Pacetti, Ariel Martin
title Heegner points on Cartan non-split curves
title_short Heegner points on Cartan non-split curves
title_full Heegner points on Cartan non-split curves
title_fullStr Heegner points on Cartan non-split curves
title_full_unstemmed Heegner points on Cartan non-split curves
title_sort heegner points on cartan non-split curves
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0008414X_v68_n2_p422_Kohen
http://hdl.handle.net/20.500.12110/paper_0008414X_v68_n2_p422_Kohen
work_keys_str_mv AT pacettiarielmartin heegnerpointsoncartannonsplitcurves
_version_ 1768543927422418944

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