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.
"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