# The Waldspurger Formula and the Gross-Zagier Formula

 SPECIAL JOINT PU/IAS NUMBER THEORY SEMINAR Topic: The Waldspurger Formula and the Gross-Zagier Formula Speaker: Xinyi Yuan Affiliation: Columbia University Date: Friday, January 25 Time/Room: 3:00pm - 4:00pm/314 Fine Hall

For the Rankin-Selberg L-function L(s, , ), there are central value formulas or derivative formulas depending on its root number. Using theta-lifting, Waldspurger showed an explicit formula relating the central value to certain period integral. We follow Waldspurgers framework to get an identity between the central derivative and the height pairing of CM points on certain Shimura curves. Many cases were proved by Gross-Zagier and S. Zhang under some unramied assumptions. Our new formula works for all ramied cases. It is a joint work with Shou-wu Zhang and Wei Zhang.