On primes in arithmetic progression having a prescribed primitive root. II

TL;DR

This paper explicitly evaluates the natural density of primes in arithmetic progression with a prescribed primitive root, under GRH, using an Euler product formula.

Contribution

It provides an explicit formula for the density of such primes, extending previous results by Lenstra under the GRH.

Findings

Explicit Euler product formula for the density of primes with given primitive root in arithmetic progression.

Conditional result assuming the Generalized Riemann Hypothesis.

Enhances understanding of the distribution of primes with specific primitive roots.

Abstract

Let a and f be coprime positive integers. Let g be an integer. Under the Generalized Riemann Hypothesis (GRH) it follows by a result of H.W. Lenstra that the set of primes p such that p=a(mod f) and g is a primitive root modulo p has a natural density. In this note this density is explicitly evaluated with an Euler product as result.