Density of the "quasi $r$-rank Artin problem"
Number Theory
2020-06-04 v2
Abstract
For a given finitely generated multiplicative subgroup of the rationals which possibly contain negative numbers, we derive, subject to GRH, formulas for the densities of primes for which the index of the reduction group has a given value. We completely classify the cases of rank one torsion groups for which the density vanishes and the the set of primes for which the index of the reduction group has a given value, is finite. For higher rank groups we propose some partial results. Finally, we propose some computations of examples comparing the approximated density computed with primes up to and that predicted by the Riemann Hypothesis.
Keywords
Cite
@article{arxiv.2006.00541,
title = {Density of the "quasi $r$-rank Artin problem"},
author = {Herish Abdullah and Andam Ali Mustafa and Francesco Pappalardi},
journal= {arXiv preprint arXiv:2006.00541},
year = {2020}
}
Comments
17 pages