THE SUM-OF-DIGITS FUNCTION FOR COMPLEX BASES

Authors
GRABNER PJ KIRSCHENHOFER P PRODINGER H
Citation
Pj. Grabner et al., THE SUM-OF-DIGITS FUNCTION FOR COMPLEX BASES, Journal of the London Mathematical Society, 57, 1998, pp. 20-40
Citations number
24
Categorie Soggetti
Mathematics,Mathematics
Journal title
Journal of the London Mathematical Society → ACNP
ISSN journal
00246107
Volume
57
Year of publication
1998
Part
1
Pages
20 - 40
Database
ISI
SICI code
0024-6107(1998)57:<20:TSFFCB>2.0.ZU;2-C
Abstract
We consider digital expansions with respect to complex integer bases. We derive precise information about the length of these expansions and the corresponding sum-of-digits function. Furthermore we give an asym ptotic formula for the sum-of-digits function in large circles and pro ve that this function is uniformly distributed with respect to the arg ument. Finally the summatory function of the sum-of-digits function al ong the real axis is analyzed.