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arXiv · 1403.7801

Heegner points on Cartan non-split curves

Daniel Kohen·Ariel Pacetti
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Abstract

Let $E$ 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 $p^2 \mid\mid N$, and $p$ is inert in $O$. Although there are no Heegner points on $X_0(N)$ 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 in Cartan non-split curves, and prove that the constructed points form a Heegner system as in the classical case.

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BibTeXRIS

Daniel Kohen, Ariel Pacetti. 2014-03-30. Heegner points on Cartan non-split curves. https://doi.org/10.4153/cjm-2015-047-6

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