| Title |
On Littlewood and Newman polynomial multiples of Borwein polynomials |
| Authors |
Drungilas, Paulius ; Jankauskas, Jonas ; Šiurys, Jonas |
| DOI |
10.1090/mcom/3258 |
| Full Text |
|
| Is Part of |
Mathematics of computation.. Providence : American Mathematical Society. 2018, Vol. 87, no 311, p. 1523-1541.. ISSN 0025-5718. eISSN 1088-6842 |
| Keywords [eng] |
Borwein polynomial ; Littlewood polynomial ; Newman polynomial ; Pisot number ; Salem number ; Mahler measure ; polynomials of small height |
| Abstract [eng] |
A Newman polynomial has all the coefficients in {0, 1} and constant term 1, whereas a Littlewood polynomial has all coefficients in {-1, 1}. We call P(X) is an element of Z[X] a Borwein polynomial if all its coefficients belong to {-1, 0, 1} and P(0) not equal 0. By exploiting an algorithm which decides whether a given monic integer polynomial with no roots on the unit circle vertical bar z vertical bar = 1 has a non-zero multiple in Z[X] with coefficients in a finite set D subset of Z, for every Borwein polynomial of degree at most 9 we determine whether it divides any Littlewood or Newman polynomial. In particular, we show that every Borwein polynomial of degree at most 8 which divides some Newman polynomial divides some Littlewood polynomial as well. In addition to this, for every Newman polynomial of degree at most 11, we check whether it has a Littlewood multiple, extending the previous results of Borwein, Hare, Mossinghoff, Dubickas and Jankauskas. |
| Published |
Providence : American Mathematical Society |
| Type |
Journal article |
| Language |
English |
| Publication date |
2018 |
| CC license |
|
