Heegner points on Cartan non-split curves
Number Theory
2019-08-15 v3
Abstract
Let be an elliptic curve of conductor , and let be an imaginary quadratic field such that the root number of is . Let be an order in and assume that there exists an odd prime , such that , and is inert in . Although there are no Heegner points on attached to , 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 in Cartan non-split curves, and prove that the constructed points form a Heegner system as in the classical case.
Keywords
Cite
@article{arxiv.1403.7801,
title = {Heegner points on Cartan non-split curves},
author = {Daniel Kohen and Ariel Pacetti},
journal= {arXiv preprint arXiv:1403.7801},
year = {2019}
}
Comments
25 pages, revised version