Joint IAS/Princeton University Number Theory Seminar

For a general L-function, the bound on its critical line obtained by applying the Phragmen-Lindeloff interpolation method is called the convexity bound. Any bounds with a power saving of the convexitybound are called subconvexity bounds. In this talk we will give the first subconvexity bounds for GL(3) L-functions as well as for GL(3) x GL(2) L-functions. Our methods also recover the subconvexity bounds for GL(2) L-functions in the eigenvalue aspect.