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September 2021 Density of the quasi $r$-rank Artin problem
Abdullah Herish, Mustafa Andam Ali, Pappalardi Francesco
Funct. Approx. Comment. Math. 65(1): 73-93 (September 2021). DOI: 10.7169/facm/1902

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 present some computations comparing the approximated density computed with primes up to $10^{10}$ and those predicted by the Riemann Hypothesis.

Citation

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Abdullah Herish. Mustafa Andam Ali. Pappalardi Francesco. "Density of the quasi $r$-rank Artin problem." Funct. Approx. Comment. Math. 65 (1) 73 - 93, September 2021. https://doi.org/10.7169/facm/1902

Information

Published: September 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.7169/facm/1902

Subjects:
Primary: 11A07
Secondary: 11N37

Rights: Copyright © 2021 Adam Mickiewicz University

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Vol.65 • No. 1 • September 2021
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