Efficient calculation of stark-heegner points via overconvergent modular symbols

This note presents a qualitative improvement to the algorithm presented in [DG] for computing Stark-Heegner points attached to an elliptic curve and a real quadratic field. This algorithm computes the Stark-Heegner point with a p-adic accuracy of M significant digits in time which is polynomial in M, the prime p being treated as a constant, rather than the O(p^M) operations required for the more naive approach taken in [DG]. The key to this improvement lies in the theory of overconvergent modular symbols developed in [PS1] and [PS2].