A unified and improved Chebotarev density theorem

Thorner, Jesse; Zaman, Asif

doi:10.2140/ant.2019.13.1039

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

A unified and improved Chebotarev density theorem

Jesse Thorner and Asif Zaman

Vol. 13 (2019), No. 5, 1039–1068

DOI: 10.2140/ant.2019.13.1039

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.

Keywords

distribution of primes, Chebotarev density theorem, effective, uniform, binary quadratic forms

Mathematical Subject Classification 2010

Primary: 11R44

Milestones

Received: 22 March 2018

Revised: 29 November 2018

Accepted: 30 January 2019

Published: 12 July 2019

Authors

Jesse Thorner
Department of Mathematics Stanford University Stanford, CA United States

Asif Zaman
Department of Mathematics Stanford University Stanford, CA United States

Vol. 13, No. 5, 2019