Arithmetic Homogeneous Spaces

A celebrated result of Waldspurger provides a relation between Fourier coefficients of half-integral weight modular forms and the central value of L-functions of the associated Shimura lift (which is a modular form of integral weight). This has a lot of arithmetic applications (which we will not discuss). My purpose in the talk is to describe 1. the representation theoretic framework behind the Shimura lift, 2. Jacquet's trace formula approach for Waldspurger's formula, 3. a higher rank generalization. (joint with Baruch and Mao.)