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March 2019 Optimal groups for the $r$-rank Artin Conjecture
Leonardo Cangelmi, Raffaele Marcovecchio
Funct. Approx. Comment. Math. 60(1): 77-86 (March 2019). DOI: 10.7169/facm/1689

Abstract

For any finitely generated subgroup $\Gamma$ of $\mathbb{Q}^*$, Pappalardi and the first--named author [1] found a formula to compute the density of the primes $\ell$ for which the reduction modulo $\ell$ of $\Gamma$ contains a primitive root modulo $\ell$. They conjectured a characterization of optimal groups, free or torsion, i.e. subgroups with maximal density. In this paper we prove their conjecture and give a similar characterization for optimal positive groups.

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Leonardo Cangelmi. Raffaele Marcovecchio. "Optimal groups for the $r$-rank Artin Conjecture." Funct. Approx. Comment. Math. 60 (1) 77 - 86, March 2019. https://doi.org/10.7169/facm/1689

Information

Published: March 2019
First available in Project Euclid: 28 March 2018

zbMATH: 07055565
MathSciNet: MR3932605
Digital Object Identifier: 10.7169/facm/1689

Subjects:
Primary: 11A07
Secondary: 11R45 , 20K15

Keywords: Artin primitive root conjecture , finitely generated subgroups of $\mathbb{Q}^*$

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.60 • No. 1 • March 2019
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