Number Theory Seminar
Jing Long Hoelscher
UIC
Bernoulli numbers and class numbers of cyclotomic function fields
Abstract: This talk will concern the divisibility of class numbers of cyclotomic
function fields and their relation with Bernoulli numbers for rational
function fields over finite fields. In number fields, the Herbrand-Ribet
theorem gives a precise relation between the divisibility of class numbers
of cyclotomic number fields and Bernoulli numbers. In function fields, the
Herbrand's direction has been proven to be true, but the other direction
has obvious counter-examples. Gekeler reformulated a conjecture similar to
Ribet's theorem. This talk will report some recent progress towards the
Gekeler's conjecture.
Wednesday October 27, 2010 at 2:00 PM in SEO 427