On primitive roots for Carlitz modules
Journal
Journal of Number Theory
Journal Volume
100
Journal Issue
1
Pages
88-103
Date Issued
2003
Author(s)
Abstract
Let A be the polynomial ring over a finite field. We prove that for every element a of a global A-field of finite A-characteristic the set of places B for which a is a primitive root under the Carlitz action possesses a Dirichlet density. We also give a criterion for this density to be positive. This is an analogue of Bilharz' version of the primitive roots conjecture of Artin, with Gm replaced by the Carlitz module. © 2003 Elsevier Science (USA). All rights reserved.
Type
journal article