Reference : Kummer theory for number fields and the reductions of algebraic numbers II
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/36399
 Title : Kummer theory for number fields and the reductions of algebraic numbers II Language : English Author, co-author : Perucca, Antonella [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Sgobba, Pietro [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : 2020 Journal title : Uniform Distribution Theory Peer reviewed : Yes Audience : International Keywords : [en] number field ; reduction ; multiplicative order ; arithmetic progression ; density Abstract : [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. We prove that the density of primes for which the condition holds is, under some general assumptions, a computable rational number which is strictly positive. We have also discovered the following equidistribution property: if \ell^e is a prime power and a is a multiple of \ell (and a is a multiple of 4 if \ell=2), then the density of primes p of K such that the order of (G mod p) is congruent to a modulo \ell^e only depends on a through its \ell-adic valuation. Target : Researchers Permalink : http://hdl.handle.net/10993/36399

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