Primes in Arithmetic Progressions and Nonprimitive Roots
Year: 2019
Type: article
Abstract: Let $p$ be a prime. If an integer $g$ generates a subgroup of index $t$ in $(\mathbb{Z}/p\mathbb{Z})^{\ast },$ then we say that $g$ is a $t$ -near primitive root modulo $p$ . We point out the easy result that each coprime residue class contains a subset of primes $p$ of positive natural density which do not have $g$ as a $t$ -near primitive root and we prove a more difficult variant.
Authors: PIETER MOREE, MIN SHA
Institutions: Max Planck Institute for Mathematics, Macquarie University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,500
OpenAlex ID: W2952452393