For any finitely generated subgroupΓofQ* we compute a formula for the density of the primes for which the reduction modulopofΓcontains a primitive root modulop. We use this to conjecture a characterization of “optimal” subgroups (i.e., subgroups that have maximal density). We also improve the error term in the asymptotic formula of Pappalardi's Theorem 1.1 (Math. Comp.66(1997), 853–868).
L., C., Pappalardi, F. (1999). On the r-rank Artin Conjecture II. JOURNAL OF NUMBER THEORY, 75(1), 120-132 [10.1006/jnth.1998.2319].
On the r-rank Artin Conjecture II
PAPPALARDI, FRANCESCO
1999-01-01
Abstract
For any finitely generated subgroupΓofQ* we compute a formula for the density of the primes for which the reduction modulopofΓcontains a primitive root modulop. We use this to conjecture a characterization of “optimal” subgroups (i.e., subgroups that have maximal density). We also improve the error term in the asymptotic formula of Pappalardi's Theorem 1.1 (Math. Comp.66(1997), 853–868).File in questo prodotto:
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