Uniformly counting primes with a given primitive root and in an arithmetic progression
Number Theory
2018-10-16 v2
Abstract
We study the number of primes with a given primitive root and in an arithmetic progression under the assumption of a suitable form of the generalized Riemann Hypothesis. Previous work of Lenstra, Moree and Stevenhagen has given asymptotics without an explicit error term, we provide an explicit error term by combining their work with the method of Hooley regarding Artin's primitive root conjecture. We give an application to a Diophantine problem involving primes with a given primitive root.
Cite
@article{arxiv.1810.04942,
title = {Uniformly counting primes with a given primitive root and in an arithmetic progression},
author = {Michel Zoeteman},
journal= {arXiv preprint arXiv:1810.04942},
year = {2018}
}
Comments
18 pages; Corrected error in the references