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 , where the integers 1 ≤ r₁ < ⋯ < r₅ ≤ d satisfy some restrictions including for j = 1,2,3,4. This result improves the previous lower bound cd³ and seems to be closer to the correct value of this function in d than the best known upper bound which is exponential in d.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-3,
author = {Art\=uras Dubickas and Jonas Jankauskas},
title = {Nonreciprocal algebraic numbers of small Mahler's measure},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {357-364},
zbl = {1284.11137},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-3}
}
Artūras Dubickas; Jonas Jankauskas. Nonreciprocal algebraic numbers of small Mahler's measure. Acta Arithmetica, Tome 161 (2013) pp. 357-364. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-3/