On primitive roots for rank one Drinfeld modules
Journal
Journal of Number Theory
Journal Volume
130
Journal Issue
2
Pages
370-385
Date Issued
2010
Author(s)
Yao, W.-C.
Abstract
Let k be a global function field over a finite field and let A be the ring of the elements in k regular outside a fixed place ∞. Let K be a global A-field of finite A-characteristic and let φ{symbol} be a rank one Drinfeld A-module over K. Given any α ∈ K, we show that the set of places P of K for which α is a primitive root modulo P under the action of φ{symbol} possesses a Dirichlet density. We also give conditions for this density to be positive. © 2009 Elsevier Inc. All rights reserved.
Type
journal article