Geodesic
A Class of Discrete Spectra of Non-Pisot Numbers
Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 9 .

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

We investigate the class of $\pm1$ polynomials evaluated at $q$ defined as: \[ A(q)=\{\epsilon_0+\epsilon_1q+\cdots+\epsilon_m q^m :\epsilon_i\in\{-1,1\}\} \] and usually called spectrum, and show that, if $q$ is the root of the polynomial $x^n-x^{n-1}-\dots-x^{k+1}+x^k+x^{k-1}+\cdots+x+1$ between 1 and 2, and $n>2k+3$, then $A(q)$ is discrete, which means that it does not have any accumulation points.
DOI : 10.2298/PIM0897009S
Classification : 11R06 11Y60
Keywords: Pisot numbers, spectra 
@article{10_2298_PIM0897009S,
     author = {Dragan Stankov},
     title = {A {Class} of {Discrete} {Spectra} of {Non-Pisot} {Numbers}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {9 },
     publisher = {mathdoc},
     volume = {_N_S_83},
     number = {97},
     year = {2008},
     doi = {10.2298/PIM0897009S},
     zbl = {1274.11160},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0897009S/}
}
TY  - JOUR
AU  - Dragan Stankov
TI  - A Class of Discrete Spectra of Non-Pisot Numbers
JO  - Publications de l'Institut Mathématique
PY  - 2008
SP  - 9 
VL  - _N_S_83
IS  - 97
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0897009S/
DO  - 10.2298/PIM0897009S
LA  - en
ID  - 10_2298_PIM0897009S
ER  - 
%0 Journal Article
%A Dragan Stankov
%T A Class of Discrete Spectra of Non-Pisot Numbers
%J Publications de l'Institut Mathématique
%D 2008
%P 9 
%V _N_S_83
%N 97
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0897009S/
%R 10.2298/PIM0897009S
%G en
%F 10_2298_PIM0897009S
Dragan Stankov. A Class of Discrete Spectra of Non-Pisot Numbers. Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 9 . doi : 10.2298/PIM0897009S. http://geodesic.mathdoc.fr/articles/10.2298/PIM0897009S/

Cité par Sources :