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Thorner, Jesse; Zaman, Asif

An explicit bound for the least prime ideal in the Chebotarev density theorem. (English) Zbl 1432.11167

Algebra Number Theory 11, No. 5, 1135-1197 (2017).
Summary: 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.

Cited in 2 Reviews
Cited in 14 Documents

MSC:

11R44 Distribution of prime ideals
11M41 Other Dirichlet series and zeta functions
14H52 Elliptic curves

Keywords:

Chebotarev density theorem; least prime ideal; Linnik’s theorem; binary quadratic forms; elliptic curves; modular forms; log-free zero density estimate
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\textit{J. Thorner} and \textit{A. Zaman}, Algebra Number Theory 11, No. 5, 1135--1197 (2017; Zbl 1432.11167)
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