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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: [email protected]
PETER KIRSCHENHOFER
Affiliation:
Institut für Mathematik und Angewandte Geometrie, Montanuniversität Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria. E-mail: [email protected]
HELMUT PRODINGER
Affiliation:
Institut für Algebra und Diskrete Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8–10, 1040 Wien, Austria. E-mail: [email protected]
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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

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