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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0008414X_v68_n2_p422_Kohen |
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todo:paper_0008414X_v68_n2_p422_Kohen2023-10-03T14:06:01Z Heegner points on Cartan non-split curves Kohen, D. Pacetti, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Kohen, D. Pacetti, A. 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. |
| format |
JOUR |
| author |
Kohen, D. Pacetti, A. |
| author_facet |
Kohen, D. Pacetti, A. |
| author_sort |
Kohen, D. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_0008414X_v68_n2_p422_Kohen |
| work_keys_str_mv |
AT kohend heegnerpointsoncartannonsplitcurves AT pacettia heegnerpointsoncartannonsplitcurves |
| _version_ |
1807315721773907968 |