We prove that the Mahler measure of an algebraic number cannot be too close to an integer, unless we have equality. The examples of certain Pisot numbers show that the respective inequality is sharp up to a constant. All cases when the measure is equal to the integer are described in terms of the minimal polynomials.

Keywords:

Mahler measure, PV numbers, Salem numbers Mahler measure, PV numbers, Salem numbers

MSC Classifications:

11R04, 11R06, 11R09, 11J68 show english descriptions Algebraic numbers; rings of algebraic integers
PV-numbers and generalizations; other special algebraic numbers; Mahler measure
Polynomials (irreducibility, etc.)
Approximation to algebraic numbers 11R04 - Algebraic numbers; rings of algebraic integers
11R06 - PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11R09 - Polynomials (irreducibility, etc.)
11J68 - Approximation to algebraic numbers

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