Bounding the least prime ideal in the Chebotarev Density Theorem

Abstract

Let $L$ be a finite Galois extension of the number field $K$. We unconditionally bound the least prime ideal of $K$ occurring in the Chebotarev Density Theorem as a power of the discriminant of $L$ with an explicit exponent. We also establish a quantitative Deuring-Heilbronn phenomenon for the Dedekind zeta function.Comment: 23 pages; v3 corrects typos and improves Theorem 1.3 & Corollary 1.4; accepted at Funct. Approx. Comment. Math. (2017