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2017 An explicit bound for the least prime ideal in the Chebotarev density theorem
Jesse Thorner, Asif Zaman
Algebra Number Theory 11(5): 1135-1197 (2017). DOI: 10.2140/ant.2017.11.1135

Abstract

We prove an explicit version of Weiss’ bound on the least norm of a prime ideal in the Chebotarev density theorem, which is a significant improvement on the work of Lagarias, Montgomery, and Odlyzko. As an application, we prove the first explicit, nontrivial, and unconditional upper bound for the least prime represented by a positive-definite primitive binary quadratic form. We also consider applications to elliptic curves and congruences for the Fourier coefficients of holomorphic cuspidal modular forms.

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Jesse Thorner. Asif Zaman. "An explicit bound for the least prime ideal in the Chebotarev density theorem." Algebra Number Theory 11 (5) 1135 - 1197, 2017. https://doi.org/10.2140/ant.2017.11.1135

Information

Received: 12 May 2016; Revised: 25 October 2016; Accepted: 10 March 2017; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06748168
MathSciNet: MR3671433
Digital Object Identifier: 10.2140/ant.2017.11.1135

Subjects:
Primary: 11R44
Secondary: 11M41 , 14H52

Keywords: binary quadratic forms , Chebotarev density theorem , Elliptic curves , least prime ideal , Linnik's theorem , log-free zero density estimate , modular forms

Rights: Copyright © 2017 Mathematical Sciences Publishers

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