Computing higher rank primitive root densities
Volume 163 / 2014
Acta Arithmetica 163 (2014), 15-32
MSC: Primary 11R45; Secondary 11L03, 11N13.
DOI: 10.4064/aa163-1-2
Abstract
We extend the “character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range of application in a systematic way.
