A degree-10 polynomial with Mahler measure approximately 1.419404632 divides no Newman polynomial, improving the upper bound on any universal constant σ such that every integer polynomial of Mahler measure less than σ divides a Newman polynomial; Newman polynomials divisible by l(x)^2 exist up to 1.
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Algorithmic aspects of Newman polynomials and their divisors
A degree-10 polynomial with Mahler measure approximately 1.419404632 divides no Newman polynomial, improving the upper bound on any universal constant σ such that every integer polynomial of Mahler measure less than σ divides a Newman polynomial; Newman polynomials divisible by l(x)^2 exist up to 1.