Fractional parts of powers of real algebraic numbers

Bugeaud, Yann

Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 459-466.

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

Classification : 11J68, 11J86, 11R06
Mots clés : Approximation to algebraic numbers, Linear forms in logarithms, Pisot number

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