Unified treatment of Artin-type problems

TL;DR

This paper introduces a comprehensive framework that unifies various versions of Artin-type problems and proves results for all of them under the Generalized Riemann Hypothesis, advancing the understanding of primitive root conjectures.

Contribution

It provides a unified approach to multiple Artin-type problems and establishes results in this broad context under GRH, extending prior isolated studies.

Findings

Unified framework for Artin-type problems

Proved results under GRH for the general setting

Extended the scope of primitive root conjecture analysis

Abstract

Since Hooley's seminal 1967 resolution of Artin's primitive root conjecture under the Generalized Riemann Hypothesis, numerous variations of the conjecture have been considered. We present a framework generalizing and unifying many previously considered variants, and prove results in this full generality (under GRH).