Mahler measure on Galois extensions

Abstract : We study the Mahler measure of generators of a Galois extension with Galois group the full symmetric group. We prove that two classical constructions of generators gives always algebraic numbers of big height. These results answer a question of C. Smyth and provide some evidence to a conjecture which asserts that the height of such a generator growth to infinity with the degree of the extension.
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Contributor : Francesco Amoroso <>
Submitted on : Monday, August 21, 2017 - 8:13:38 PM
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Francesco Amoroso. Mahler measure on Galois extensions. Bulletin of the London Mathematical Society, London Mathematical Society, 2016. ⟨hal-01575925⟩

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