Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-28T19:45:34.162Z Has data issue: false hasContentIssue false
  • English
  • Français

THE SUM-OF-DIGITS FUNCTION FOR COMPLEX BASES

Published online by Cambridge University Press:  01 February 1998

PETER J. GRABNER ,
PETER KIRSCHENHOFER  and
HELMUT PRODINGER
PETER J. GRABNER
Affiliation:
Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria. E-mail: grabner@weyl.math.tu-graz.ac.at
PETER KIRSCHENHOFER
Affiliation:
Institut für Mathematik und Angewandte Geometrie, Montanuniversität Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria. E-mail: Peter.Kirschenhofer@unileoben.ac.at
HELMUT PRODINGER
Affiliation:
Institut für Algebra und Diskrete Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8–10, 1040 Wien, Austria. E-mail: Helmut.Prodinger@tuwien.ac.at
Get access

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 asymptotic formula for the sum-of-digits function in large circles and prove that this function is uniformly distributed with respect to the argument. Finally the summatory function of the sum-of-digits function along the real axis is analyzed.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 20 - 40
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)