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 -