Number Theory Working Seminar
Abel Castillo
UIC
Effective versons of Hilbert's Irreducibility Theorem for global fields
Abstract: This talk has two goals. The first is to prove a generalization of a result of Rainer Dietmann, where we aim to count specializations of bounded height of a generic polynomial $f_t(X) \in \mathbf{Z}[t,X]$ whose Galois group is a particular subgroup of the generic polynomial. The second is to prove a function field analogue of a result of S. D. Cohen, where we aim to count specializations of bounded height of a generic polynomial $f_t(X) \in \mathcal{O}_k[t,X]$ whose Galois group equals that of the generic polynomial, where $k$ is an arbitrary global field of positive characteristic.
Wednesday May 1, 2013 at 9:30 AM in SEO 512