Metrical results on the distribution of fractional parts of powers of real numbers

Abstract : Denote by {·} the fractional part. We establish several new metrical results on the distribution properties of the sequence ({x n }) n≥1. Many of them are presented in a more general framework, in which the sequence of functions (x → x n) n≥1 is replaced by a sequence (fn) n≥1 , under some growth and regularity conditions on the functions fn.
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Submitted on : Tuesday, October 10, 2017 - 2:16:28 PM
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  • HAL Id : hal-01614076, version 1
  • ARXIV : 1710.03596

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Yann Bugeaud, Lingmin Liao, Michal Rams. Metrical results on the distribution of fractional parts of powers of real numbers. 2017. ⟨hal-01614076⟩

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