Fwd: Seminar

[William Stein]

Hi,

The Number Theory Seminar tomorrow stars Sal Baig, and will be about
ranks of elliptic curves over functions fields:

Fridays 3:30 - 4:30pm in Padelford C401

Title: The Average Analytic Rank in a Family of Quadratic Twists of an
Elliptic Curve over $\F_q(t)$

Abstract: The $L$-function of a non-isotrivial elliptic curve over a
function field of positive characteristic is known to be a polynomial
with integer coefficients. Its analytic rank can be thus computed
exactly, providing data to test the validity of Goldfeld's conjecture
in the function field case. This conjecture claims that the average
rank in a family of a quadratic twists of a fixed elliptic curve
approaches 1/2 as the degree $d$ of the twisting polynomials increase.
We (for the most part) show that this average rank is at least 1/2 as
$d\rightarrow\infty$.

--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org