Special Colloquium
Kartik Prasanna
UCLA
Elliptic curves, quadratic twists and L-values
Abstract: The first half of the talk will be an elementary discussion
of elliptic curves, their associated L-functions and the structure of
the Birch and Swinnerton-Dyer conjecture (BSD) for the behaviour of
such L-functions at the central point s=1.
In the second half, I will begin by explaining a theorem of
Waldspurger on nonvanishing of central values of quadratic twists, and
its applications, most notably to BSD. Finally, I will formulate a
conjectural "mod p" analog of Waldspurger's theorem and describe some
recent results that are related to this problem.
Monday January 30, 2006 at 4:00 PM in SEO 636