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On the order of the reductions of algebraic numbers
Sgobba, Pietro
2020
 

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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. 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.
Disciplines :
Mathematics
Author, co-author :
Sgobba, Pietro ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
On the order of the reductions of algebraic numbers
Publication date :
06 February 2020
Event name :
Seminari de Teoria de Nombres de Barcelona 2020
Event date :
from 03-02-2020 to 07-02-2020
Available on ORBilu :
since 12 February 2020

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