CONICET | Buscador de Institutos y Recursos Humanos

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 p^2∣∣ 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.