Functional Limit Theorems for Digital Expansions

نویسندگان

  • MICHAEL DRMOTA
  • MICHAEL FUCHS
چکیده

The main purpose of this paper is to discuss the asymptotic behavior 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’s 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.

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تاریخ انتشار 2002