An effective Chebotarev density theorem under GRH

TL;DR

This paper proves an effective Chebotarev density theorem assuming the Riemann hypothesis for Dedekind zeta functions, providing explicit bounds on the distribution of prime ideals with a given Artin symbol.

Contribution

It offers a new effective version of the Chebotarev density theorem under GRH, improving explicit bounds on prime ideal distribution.

Findings

Established an explicit bound for prime ideal density under GRH

Extended Chebotarev theorem to an effective form with concrete estimates

Assumed Riemann hypothesis for Dedekind zeta functions to derive results

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.