On the density of primes in arithmetic progression having a prescribed primitive root

1999/12/07 by Pieter Moree, Moree, Pieter
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/9912252

arxiv created 1999/12/07 · openalex publication_date 1999/12/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a,f and g be integers, with a and f coprime. Under the generalized Riemann hypothesis it follows from work of Hooley and Lenstra that the set of primes p such that p=a(mod f) and g is primitive root mod p has a natural density. In this note we explicitly evaluate this density and give some applications of this result.

Related

• Uniformly counting primes with a given primitive root and in an\n arithmetic progression
• Refinements of Artin's primitive root conjecture
• The Least Prime Primitive Root and the Shifted Sieve
• Uniform bounds for the density in Artin's conjecture on primitive roots
• Simple Proof of the Primitive Root Conjecture