Log-free zero density estimates for automorphic L-functions

Abstract

We prove a log-free zero density estimate for automorphic L-functions defined over a number field k. This work generalizes and sharpens the method of pseudo-characters and the large sieve used earlier by Kowalski and Michel. As applications, we demonstrate for a particular family of number fields of degree n over k (for any n) that an effective Chebotarev density theorem and a bound on ℓ-torsion in class groups hold for almost all fields in the family.