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• # Artykuł - szczegóły

## Acta Arithmetica

2013 | 157 | 4 | 357-364

## Nonreciprocal algebraic numbers of small Mahler's measure

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.

357-364

wydano
2013

### Twórcy

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