Salem numbers as Mahler measures of nonreciprocal units (Q2833608)
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scientific article; zbMATH DE number 6654767
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Salem numbers as Mahler measures of nonreciprocal units |
scientific article; zbMATH DE number 6654767 |
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Salem numbers as Mahler measures of nonreciprocal units (English)
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18 November 2016
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Salem numbers
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Mahler measure
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non-reciprocal polynomial
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Galois group
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The author studies the set \(L_0\) consisting of Mahler measures of non-reciprocal polynomials \(f\in \mathbb Z[X]\), shows in Sect. 3 that the Mahler measure of \(X^4+(kX-1)^2\) is of degree 4, being a root of \(X^4-k^2X^3=2X^2-k^2X+1\), thus \(L_0\) contains infinitely many Salem numbers of degree \(4\), and establishes in Sect. 4 that \(L_0\) contains infinitely many Salem numbers of degree \(4m+2\) for \(m=1,2,\dots\).
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