Titlebook: Around the Unit Circle; Mahler Measure, Inte James McKee,Chris Smyth Textbook 2021 Springer Nature Switzerland AG 2021 Mahler measure.Lehme

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https://doi.org/10.1007/978-981-16-4404-7We show that the Mahler measure of a nonreciprocal integer polynomial has its minimum value for the polynomial ., and that this value is an isolated point in the set of such measures.

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Mahler Measures of Polynomials in One Variable,In this chapter, we introduce some basic results about the Mahler measure of polynomials in one variable and some of its applications. In later chapters, there are further results for one-variable Mahler measures: Dobrowolski’s Theorem and Mahler measures for restricted sets of polynomials and for nonreciprocal polynomials.

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,Dobrowolski’s Theorem,We prove Dobrowolski’s famous lower bound for the Mahler measure of an algebraic number of degree . and Mahler measure greater than 1. We follow the proof of Cantor and Straus, based on the confluent Vandermonde determinant.

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