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Metrical Results on the Distribution of Fractional Parts of Powers of Real Numbers

Published online by Cambridge University Press:  29 November 2018

Yann Bugeaud
Affiliation:
IRMA UMR 7501, CNRS, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France ([email protected])
Lingmin Liao
Affiliation:
LAMA UMR 8050, CNRS, Université Paris-Est Créteil, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France ([email protected])
Michał Rams
Affiliation:
Institute of Mathematics Polish Academy of Sciences ul. Śniadeckich 8, 00-656 Warszawa, Poland ([email protected])

Abstract

We establish several new metrical results on the distribution properties of the sequence ({xn})n≥1, where {·} denotes the fractional part. Many of them are presented in a more general framework, in which the sequence of functions (xxn)n≥1 is replaced by a sequence (fn)n≥1, under some growth and regularity conditions on the functions fn.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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