2020/05/31 by Herish Abdullah, Abdullah, Herish, Andam Ali Mustafa +3
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2006.00541
openalex publication_date 2020/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 1010 and that predicted by the Riemann Hypothesis.