α-expansions, linear recurrences, and the sum-of-digits function

Peter J. Grabner; Robert F. Tichy

doi:10.1007/BF02568381

α-expansions, linear recurrences, and the sum-of-digits function

Peter J. Grabner^*, Robert F. Tichy

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We give a generalization of the ordinary q-ary digit expansion of positive integers to arbitrary real bases α>1. We investigate the properties of the sum-of-digit function s(n). We give an asymptotic formula for the sum ∑_n<N s(itn) and consider the distribution properties of the sequence xs(n) for irrational x.

Original language	English
Pages (from-to)	311-324
Number of pages	14
Journal	Manuscripta mathematica
Volume	70
Issue number	1
DOIs	https://doi.org/10.1007/BF02568381
Publication status	Published - 1 Dec 1991

ASJC Scopus subject areas

Mathematics(all)

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10.1007/BF02568381

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title = "α-expansions, linear recurrences, and the sum-of-digits function",

abstract = "We give a generalization of the ordinary q-ary digit expansion of positive integers to arbitrary real bases α>1. We investigate the properties of the sum-of-digit function s(n). We give an asymptotic formula for the sum ∑ n<N s(itn) and consider the distribution properties of the sequence xs(n) for irrational x.",

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N2 - We give a generalization of the ordinary q-ary digit expansion of positive integers to arbitrary real bases α>1. We investigate the properties of the sum-of-digit function s(n). We give an asymptotic formula for the sum ∑ n<N s(itn) and consider the distribution properties of the sequence xs(n) for irrational x.

AB - We give a generalization of the ordinary q-ary digit expansion of positive integers to arbitrary real bases α>1. We investigate the properties of the sum-of-digit function s(n). We give an asymptotic formula for the sum ∑ n<N s(itn) and consider the distribution properties of the sequence xs(n) for irrational x.

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α-expansions, linear recurrences, and the sum-of-digits function

Abstract

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