An effective Chebotarev density theorem under GRH

Abstract

We prove an effective version of the Chebotarev theorem for the density of prime ideals with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions.

arXiv commentAfter the publication of this paper we have discovered a misprint in Eq.(3.4). The misprint does not affect the validity of the theorems and corollaries proved in the paper, but the values of some constants appearing in several equations need to be changed. This version of the paper corrects all of them

References in corpus (3)

• Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH
• Explicit smoothed prime ideals theorems under GRH
• Théorème de Chebotarev effectif

Cited by in corpus (6)

• Unconditional Explicit Mertens' Theorems for Number Fields and Dedekind Zeta Residue Bounds
• Distribution of Frobenius elements in families of Galois extensions
• Chebotarev density theorem in short intervals for extensions of ${\mathbb{F}}_q(T)$
• Explicit upper bounds on the average of Euler-Kronecker constants of narrow ray class fields
• Endomorphism rings of supersingular elliptic curves over ${\mathbb{F}}_p$
• The rightness of the Riemann Hypothesis