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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Derivatives of L-functions and infinite products

Presented by Jan Bruinier, TU Darmstadt (Germany)

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.

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