Abstract: Attached to any modular form f that is not ordinary at p one can construct two p-adic L-functions. However, when f is ordinary at p the standard constructions yield only one p-adic L-function. Where is this other L-function? In this talk, we will use overconvergent modular symbols to construct the p-adic L-function attached to the evil twin of an ordinary form.

Given an elliptic curve and a supersingular prime p one can attach two p-adic L-functions