Given a multiplicative group of non zero rational numbers and a positive integer m , we consider the problem of determining the density of the set of primes p for which the order of the reduction modulo p of the group is divisible by m . In the case when the group is nitely generated the density is explicitly computed. Some example of groups with innite rank are considered.
Pappalardi, F. (2015). Divisibility of reduction in groups of rational numbers. MATHEMATICS OF COMPUTATION, 84(291), 385-407 [10.1090/S0025-5718-2014-02872-X].
Divisibility of reduction in groups of rational numbers
PAPPALARDI, FRANCESCO
2015-01-01
Abstract
Given a multiplicative group of non zero rational numbers and a positive integer m , we consider the problem of determining the density of the set of primes p for which the order of the reduction modulo p of the group is divisible by m . In the case when the group is nitely generated the density is explicitly computed. Some example of groups with innite rank are considered.File in questo prodotto:
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