Abstract
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 language | English |
|---|---|
| Pages (from-to) | 175-201 |
| Number of pages | 27 |
| Journal | Acta Mathematica Hungarica |
| Volume | 98 |
| Issue number | 3 |
| DOIs | |
| 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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Drmota, M., Fuchs, M., & Manstavičius, E. (2002). Functional limit theorems for digital expansions. Acta Mathematica Hungarica, 98(3), 175-201. https://doi.org/10.1023/A:1022869708089