Thirteenth Algorithmic Number Theory Symposium ANTS-XIII University of Wisconsin, Madison July 16 – 20, 2018 Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII) July 16 – 20, 2018

Effective Chebotarev density theorems for families of number fields without GRH

Melanie Matchett Wood

Abstract: We discuss a new effective Chebotarev density theorem, not conditional on GRH, that improves the previously known unconditional error term and allows primes to be taken quite small; this theorem holds for the Galois closures of "almost all" number fields that lie in an appropriate family of field extensions. We discuss applications to bounds on l-torsion in the class groups and small generators for number fields. This talk is on joint work with Lillian Pierce and Caroline Turnage-Butterbaugh.

Files available: slides