Comptes Rendus
Number theory
Fractional parts of powers of real algebraic numbers
Comptes Rendus. Mathématique, Volume 360 (2022), 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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.314
Classification: 11J68, 11J86, 11R06
Keywords: Approximation to algebraic numbers, Linear forms in logarithms, Pisot number
Yann Bugeaud 1, 2

1 Institut universitaire de France
2 Université de Strasbourg, Mathématiques, 7 rue René Descartes, 67084 Strasbourg, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Yann Bugeaud. Fractional parts of powers of real algebraic numbers. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 459-466. doi : 10.5802/crmath.314. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.314/

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