Théorie des nombres
Fractional parts of powers of real algebraic numbers
Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 459-466.

Let α be a real algebraic number greater than 1. We establish an effective lower bound for the distance between an integral power of α and its nearest integer.

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DOI : 10.5802/crmath.314
Classification : 11J68, 11J86, 11R06
Mots clés : Approximation to algebraic numbers, Linear forms in logarithms, Pisot number
Bugeaud, Yann 1, 2

1 Université de Strasbourg, Mathématiques, 7 rue René Descartes, 67084 Strasbourg, France
2 Institut universitaire de France
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Bugeaud, Yann. Fractional parts of powers of real algebraic numbers. Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 459-466. doi : 10.5802/crmath.314. http://www.numdam.org/articles/10.5802/crmath.314/

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