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