Number Theory Seminar: Nike Vatsal (UBC)

In a previous lecture I waved my hands at the subject of period integrals for automorphic forms on SL_2. If that lecture had a point, it was that the phenomenon of non-vanishing of quadratic twists of L-functions was somehow related to the non-vanishing of the symmetric square L-function. In this lecture, I will try to substantiate that claim by describing the relative trace formula of Jacquet, and by sketching the general shape of this formula for the group SL_2. In the end, I'll try to explain how one might get information about quadratic twists directly from the symmetric square if only one had a stable form of Jacquet's formula, and if one could explicitly evaluate the stable and kappa-stable portions.