Reference : On the order of the reductions of algebraic numbers
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On the order of the reductions of algebraic numbers
Sgobba, Pietro mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Seminari de Teoria de Nombres de Barcelona 2020
from 03-02-2020 to 07-02-2020
[en] Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. For almost all primes p of K, we consider the order of the cyclic group (G mod p), and ask whether this number lies in a given arithmetic progression. The density of primes for which this condition holds exists (this generalizes a result of Ziegler from 2006) and it is, under certain assumptions, a computable positive rational number. We also present a uniformity property concerning some special cases. This is a joint work with A. Perucca.

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