Geodesic
On the Conjugates of Certain Algebraic Integers
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 281

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A well-known theorem, due to C.\,J. Smyth, asserts that two conjugates of a Pisot number, having the same modulus are necessary complex conjugates. We show that this result remains true for $K$-Pisot numbers, where $K$ is a real algebraic number field. Also, we prove that a $j$-Pisot number, where $j$ is a natural number, can not have more than $2j$ conjugates with the same modulus.
DOI : 10.2298/PIM1613281Z
Classification : 11R06, 11R04, 12D10
Keywords: Pisot numbers, Salem numbers, special algebraic numbers 
@article{10_2298_PIM1613281Z,
     author = {Toufik Za{\"\i}mi},
     title = {On the {Conjugates} of {Certain} {Algebraic} {Integers}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {281 },
     publisher = {mathdoc},
     volume = {_N_S_99},
     number = {113},
     year = {2016},
     doi = {10.2298/PIM1613281Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM1613281Z/}
}
TY  - JOUR
AU  - Toufik Zaïmi
TI  - On the Conjugates of Certain Algebraic Integers
JO  - Publications de l'Institut Mathématique
PY  - 2016
SP  - 281 
VL  - _N_S_99
IS  - 113
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM1613281Z/
DO  - 10.2298/PIM1613281Z
LA  - en
ID  - 10_2298_PIM1613281Z
ER  - 
%0 Journal Article
%A Toufik Zaïmi
%T On the Conjugates of Certain Algebraic Integers
%J Publications de l'Institut Mathématique
%D 2016
%P 281 
%V _N_S_99
%N 113
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM1613281Z/
%R 10.2298/PIM1613281Z
%G en
%F 10_2298_PIM1613281Z
Toufik Zaïmi. On the Conjugates of Certain Algebraic Integers. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 281 . doi: 10.2298/PIM1613281Z

Cité par Sources :