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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Cyclotomic Integer Symmetric Matrices Embedded in Toroidal and Cylindrical Tessellations,Having classified all cyclotomic integer symmetric matrices (those with Mahler measure 1), we move towards the analogue of Lehmer’s conjecture for integer symmetric matrices. The main goal in this chapter is to get an improved understanding of the structure of the maximal cyclotomic examples.

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The Method of Explicit Auxiliary Functions,In this chapter, we consider bounds for various functions defined on conjugate sets of algebraic numbers. These bounds are obtained by the use of explicit auxiliary functions, which are built from the logarithms of moduli of specific polynomials.

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https://doi.org/10.1007/978-3-030-91748-7xt, we describe how to find the points on a plane curve whose coordinates are roots of unity. Then we give some fundamental results on the Cassels height of a cyclotomic integer, followed by some results on the minimal number of roots of unity whose sum is a given cyclotomic integer. Most of the res

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