## Algebra & Number Theory

### A unified and improved Chebotarev density theorem

#### Abstract

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 the 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.

#### Article information

Source
Algebra Number Theory, Volume 13, Number 5 (2019), 1039-1068.

Dates
Revised: 29 November 2018
Accepted: 30 January 2019
First available in Project Euclid: 17 July 2019

https://projecteuclid.org/euclid.ant/1563328821

Digital Object Identifier
doi:10.2140/ant.2019.13.1039

Mathematical Reviews number (MathSciNet)
MR3981313

Zentralblatt MATH identifier
07083101

Subjects

#### Citation

Thorner, Jesse; Zaman, Asif. A unified and improved Chebotarev density theorem. Algebra Number Theory 13 (2019), no. 5, 1039--1068. doi:10.2140/ant.2019.13.1039. https://projecteuclid.org/euclid.ant/1563328821

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