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On the distribution of sequences connected with digit-representation

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Abstract

Let N=e(s)b(s)+e(s−1)b(s−1)+...+e(1)b(1)+e(0) be the digit representation of the integer N to base b or to α-scale, that is with respect to the best approximation denominators of an irrational number α. Let f:N0 → Z with f(0)=0 be an arbitrary function and r(0),r(1),... be an arbitrary sequence of integers and F(N):=f(e(s))r(s)+...+f(e (1))r(1)+f(e(0))r(0). Conditions for the uniform distribution modulo one of the sequence {F(N)x}N∈N, x∈ℝ are given.

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  1. Institut für Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020, Salzburg, Austria

    Gerhard Larcher

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  1. Gerhard Larcher
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Larcher, G. On the distribution of sequences connected with digit-representation. Manuscripta Math 61, 33–42 (1988). https://doi.org/10.1007/BF01153580

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  • DOI: https://doi.org/10.1007/BF01153580

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