On certain multiples of Littlewood and Newman polynomials
Bull. Korean Math. Soc. 2018 Vol. 55, No. 5, 1491-1501
Published online September 30, 2018
Paulius Drungilas, Jonas Jankauskas, Grintas Junevicius, Lukas Klebonas, Jonas Siurys
Vilnius University, Mathematik und Statistik, Montanuniversit\"at Leoben, Vilnius University, Vilnius University, Vilnius University
Abstract : 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 $32765$.
Keywords : Borwein polynomial, Littlewood polynomial, Newman polynomial, Salem number, complex Salem number, polynomials of small height
MSC numbers : 11R09, 11Y16, 12D05, 11R06
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