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Reductions of algebraic integers

Debry, Christophe ; Perucca, Antonella



Abstract

Let K be a number field, and let G be a finitely generated subgroup of K-X. Fix some prime number l, and consider the set of primes p of K satisfying the following property: the reduction of G modulo p is well-defined and has size coprime to l. We are able to give a closed-form expression for the natural density of this set. (C) 2016 Elsevier Inc. All rights reserved.


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