BIMSA-YMSC Tsinghua Number Theory Seminar—— Reciprocity, non-vanishing, and subconvexity of central L-values

Abstract：

A reciprocity formula usually relates certain moments of two different families of L-functions which apparently have no connections between them. The first such formula was due to Motohashi who related a fourth moment of Riemann zeta values on the central line with a cubic moment of certain automorphic central L-values for GL(2). In this talk, we describe some instances of reciprocity formulas both in low and high rank groups and give certain applications to subconvexity and non-vanishing of central L-values. These are joint works with Nunes and Blomer--Nelson.