1/25/2008

Xinyi Yuan
Columbia University

The Waldspurger Formula and the Gross-Zagier Formula

For the Rankin-Selberg L-function L(s, π, χ), there are central value formulas or derivative formulas depending on its root number. Using theta-lifting, Waldspurger showed an explicit formula relating the cen- tral value to certain period integral. We follow Waldspurger’s 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 unram- ified assumptions. Our new formula works for all ramified cases. It is a joint work with Shou-wu Zhang and Wei Zhang.