Nonreciprocal algebraic numbers of small Mahler's measure

Artūras Dubickas, and Jonas Jankauskas. "Nonreciprocal algebraic numbers of small Mahler's measure." Acta Arithmetica 157.4 (2013): 357-364. <http://eudml.org/doc/286371>.

@article{ArtūrasDubickas2013,
abstract = {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 $1 + x^\{r₁\} + ⋯ + x^\{r₅\}$, where the integers 1 ≤ r₁ < ⋯ < r₅ ≤ d satisfy some restrictions including $2r_\{j\} < r_\{j+1\}$ for j = 1,2,3,4. This result improves the previous lower bound cd³ and seems to be closer to the correct value of this function in d than the best known upper bound which is exponential in d.},
author = {Artūras Dubickas, Jonas Jankauskas},
journal = {Acta Arithmetica},
keywords = {Mahler measure; irreducible polynomials},
language = {eng},
number = {4},
pages = {357-364},
title = {Nonreciprocal algebraic numbers of small Mahler's measure},
url = {http://eudml.org/doc/286371},
volume = {157},
year = {2013},
}

TY - JOUR
AU - Artūras Dubickas
AU - Jonas Jankauskas
TI - Nonreciprocal algebraic numbers of small Mahler's measure
JO - Acta Arithmetica
PY - 2013
VL - 157
IS - 4
SP - 357
EP - 364
AB - 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 $1 + x^{r₁} + ⋯ + x^{r₅}$, where the integers 1 ≤ r₁ < ⋯ < r₅ ≤ d satisfy some restrictions including $2r_{j} < r_{j+1}$ for j = 1,2,3,4. This result improves the previous lower bound cd³ and seems to be closer to the correct value of this function in d than the best known upper bound which is exponential in d.
LA - eng
KW - Mahler measure; irreducible polynomials
UR - http://eudml.org/doc/286371
ER -