Pure Maths Colloquium: Derivatives of L-functions and infinite products
3 May 2010 16:15 in CM 107
The Birch and Swinnerton-Dyer conjecture is one of the most fascinating problems in number theory, providing a link between rational points on an elliptic curve and the order of vanishing of its L-function at the center of symmetry. In our talk we discuss the Gross-Zagier formula, which is an important ingredient in the proof of the BSD conjecture for elliptic curves of analytic rank one. We show how it relates to work of Borcherds on infinite product expansions of modular forms. Generalizing Borcherds' ideas one obtains a new approach to the Gross-Zagier formula and generalizations.