Open Access
Translator Disclaimer
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


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.


Download Citation

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.


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

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


Vol.11 • No. 5 • 2017
Back to Top