A unified and improved Chebotarev density theorem

Jesse Thorner, Asif Zaman

Published 2018-03-07Version 1

We establish an unconditional effective Chebotarev density theorem that improves uniformly over the well-known result of Lagarias and Odlyzko. As a consequence, we give a new asymptotic form of Chebotarev density theorem that can count much smaller primes with arbitrary log-power savings, even in the case where a Landau-Siegel zero is present. Our main theorem also interpolates the strongest unconditional upper bound for the least prime ideal with a given Artin symbol as well as the Chebotarev analogue of the Brun-Titchmarsh theorem proved by the authors.