Some Aspects of the Theta Correspondence

ARITHMETIC HOMOGENEOUS SPACES
Topic:Some Aspects of the Theta Correspondence
Speaker:Erez Lapid
Affiliation:IAS
Date:Friday, September 30
Time/Room:11:00am - 12:30pm/S-101

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.)