On certain multiples of Littlewood and Newman polynomials
Publikationen: Beitrag in Fachzeitschrift › Artikel › Forschung › (peer-reviewed)
Standard
in: Taehan-Suhakhoe-hoebo = Bulletin of the Korean Mathematical Society, Jahrgang 55.2018, Nr. 5, 2018, S. 1491-1501.
Publikationen: Beitrag in Fachzeitschrift › Artikel › Forschung › (peer-reviewed)
Harvard
APA
Vancouver
Author
Bibtex - Download
}
RIS (suitable for import to EndNote) - Download
TY - JOUR
T1 - On certain multiples of Littlewood and Newman polynomials
AU - Drungilas, Paulius
AU - Jankauskas, Jonas
AU - Junevičius, Grintas
AU - Klebonas, Lukas
AU - Šiurys, Jonas
PY - 2018
Y1 - 2018
N2 - Polynomials with all the coefficients in {0,1} and constant term 1 are called Newman polynomials, whereas polynomials with all the coefficients in {−1,1} are called Littlewood polynomials. By exploiting an algorithm developed earlier, we determine the set of Littlewood polynomials of degree at most 12 which divide Newman polynomials. Moreover, we show that every Newman quadrinomial X^a+X^b+X^c+1, 15>a>b>c>0, has a Littlewood multiple of smallest possible degree which can be as large as 32765.
AB - Polynomials with all the coefficients in {0,1} and constant term 1 are called Newman polynomials, whereas polynomials with all the coefficients in {−1,1} are called Littlewood polynomials. By exploiting an algorithm developed earlier, we determine the set of Littlewood polynomials of degree at most 12 which divide Newman polynomials. Moreover, we show that every Newman quadrinomial X^a+X^b+X^c+1, 15>a>b>c>0, has a Littlewood multiple of smallest possible degree which can be as large as 32765.
KW - Borwein
KW - Littlewood polynomia
KW - Newman polynomials
KW - Salem Numbers
KW - complex Salem Numbers
KW - Polynomials of small height
U2 - 10.4134/BKMS.b170854
DO - 10.4134/BKMS.b170854
M3 - Article
VL - 55.2018
SP - 1491
EP - 1501
JO - Taehan-Suhakhoe-hoebo = Bulletin of the Korean Mathematical Society
JF - Taehan-Suhakhoe-hoebo = Bulletin of the Korean Mathematical Society
SN - 1015-8634
IS - 5
ER -