Nonreciprocal algebraic numbers of small Mahler's measure

• Autorzy: Artūras Dubickas , Jonas Jankauskas
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
• 11R09: Polynomials (irreducibility, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 157
• Numer: 4
• Strony: 357-364

Daty

wydano

2013

Twórcy

autor

Artūras Dubickas

• Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania

autor

Jonas Jankauskas

• Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania

Identyfikatory

DOI

10.4064/aa157-4-3