Functional limit theorems for digital expansions

M. Drmota*, Michael Fuchs, E. Manstavičius

*Corresponding author for this work

研究成果: Article同行評審

1 引文 斯高帕斯(Scopus)

摘要

The main purpose of this paper is to discuss the asymptotic behaviour of the difference sq,k (P(n)) - k(q - 1)/2 where sq,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.

原文English
頁(從 - 到)175-201
頁數27
期刊Acta Mathematica Hungarica
98
發行號3
DOIs
出版狀態Published - 1 二月 2002

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