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Nonreciprocal algebraic numbers of small Mahler's measure

Artūras Dubickas; Jonas Jankauskas — 2013

Acta Arithmetica

We prove that there exist at least cd⁵ monic irreducible nonreciprocal polynomials with integer coefficients of degree at most d whose Mahler measures are smaller than 2, where c is some absolute positive constant. These polynomials are constructed as nonreciprocal divisors of some Newman hexanomials $1 + x^{r ₁} + \dots + x^{r ₅}$ , where the integers 1 ≤ r₁ < ⋯ < r₅ ≤ d satisfy some restrictions including $2 r_{j} < r_{j + 1}$ for j = 1,2,3,4. This result improves the previous lower bound cd³ and seems to be closer to the correct value of...

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