Artūras Dubickas
Abstract
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Abstract We prove that theMahler 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.
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Abstract We prove that theMahler 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.
Key concepts: Mathematics, Integer (computer science), Measure (data warehouse), Algebraic number, Constant (computer programming), Combinatorics, Discrete mathematics, Mathematical analysis