English

Heegner points on Cartan non-split curves

Number Theory 2019-08-15 v3

Abstract

Let EE be an elliptic curve of conductor NN, and let KK be an imaginary quadratic field such that the root number of E/KE/K is 1-1. Let OO be an order in KK and assume that there exists an odd prime pp, such that p2Np^2 \mid\mid N, and pp is inert in OO. Although there are no Heegner points on X0(N)X_0(N) attached to OO, 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

R2 v1 2026-06-22T03:38:29.788Z