Acta Mathematica Hungarica
Volume/Issue:
Volume 98: Issue 3
Functional limit theorems for digital expansions
Authors:
M. Drmota Vienna University of Technology Department of Geometry Wiedner Hauptstrasse 8-10/113 A-1040 Vienna Austria

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M. Fuchs Vienna University of Technology Department of Geometry Wiedner Hauptstrasse 8-10/113 A-1040 Vienna Austria

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E. Manstavičius Vilnius University Department of Mathematics and Informatics Naugarduko STR. 24 LT 2600 Vilnius Lithuania

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Pages:
175–201
Online Publication Date:
03 Nov 2004
Publication Date:
01 Feb 2002
Article Category:
Research Article
DOI:
https://doi.org/10.1023/a:1022869708089
Keywords:
sum-of-digits function; functional limit theorem; Strassen's law of the iterated logarithm; q-ary digital expansion
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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.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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