Functional limit theorems for digital expansions

M. Drmota; Michael Fuchs; E. Manstavičius

doi:10.1023/A:1022869708089

Functional limit theorems for digital expansions

M. Drmota^*, Michael Fuchs, E. Manstavičius

^*Corresponding author for this work

Department of Applied Mathematics

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

1 Scopus citations

Abstract

The main purpose of this paper is to discuss the asymptotic behaviour of the difference s_q,k (P(n)) - k(q - 1)/2 where s_q,k(n) denotes the sum of the first k digits in the q-ary digital expansion of n and P(x) is an integer polynomial. We prove that this difference can be approximated by a Brownian motion and obtain under special assumptions on P, a Strassen type version of the law of the iterated logarithm. Furthermore, we extend these results to the joint distribution of q₁-ary and q₂-ary digital expansions where q₁ and q₂ are coprime.

Original language	English
Pages (from-to)	175-201
Number of pages	27
Journal	Acta Mathematica Hungarica
Volume	98
Issue number	3
DOIs	https://doi.org/10.1023/A:1022869708089
State	Published - 1 Feb 2002

Keywords

Functional limit theorem
Q-ary digital expansion
Strassen's law of the iterated logarithm
Sum-of-digits function

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Functional limit theorems for digital expansions

Abstract

Keywords

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