Functional limit theorems for digital expansions

M. Drmota*, Michael Fuchs, E. Manstavičius

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)175-201
Number of pages27
JournalActa Mathematica Hungarica
Issue number3
StatePublished - 1 Feb 2002


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

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