Number Theory Seminar: 2011-11-17

At 3:35pm November 17, 2011 in Padelford C-401.

NOTES: bober-nts-2011-11-17-bounding_rank.pdf

SPEAKER: Jon Bober (Univ of Washington)

TITLE: Using the explicit formula to bound ranks of elliptic curves

Abstract

I'll describe an analytic method which, assuming the Riemann hypothesis and the BSD conjecture, often gives good upper bounds for the ranks of elliptic curves. The method has its origins in the work of Mestre, and was used by Fermigier in 1996, but does not seem to have been used much since then. As an example of why it is nice I'll show how to get tight upper bounds for curves of rank 20 through 24, and will get something pretty close for a curve of rank at least 28.