On the order of the reductions of algebraic numbers

English

Sgobba, Pietro[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

6-Feb-2020

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.