Seminars & Colloquia Calendar

Abstract: The combination of the Kuznetsov and Voronoi formulas has played a powerful role in analytic estimates of automorphic L-functions for GL(2), for example in the subconvexity problem.  The talk will discuss applications of a new combination of formulas for GL(4), which yields an identity equating sums of GL(4) x GL(2) L-values with other sums of the same type.  As an application, we show that for each self-dual cusp form F on GL(4,Z)GL(4,R) there exists infinitely many Maass forms f such that L(1/2,F x f) is nonzero.  Time permitting, I will explain why techniques used in the proof suggest that the GL(n) x GL(n-2) Converse Theorem of Cogdell & Piatetski-Shapiro is sharp.