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THE SUM OF DIGITS FUNCTION IN NUMBER FIELDS

Published online by Cambridge University Press:  01 January 1998

JÖRG M. THUSWALDNER
JÖRG M. THUSWALDNER
Affiliation:
Institut für Mathematik und Angewandte Geometrie, Abteilung für Mathematik und Statistik, Montanuniversität Leoben, Franz-Josef-Straße 18, A–8700 Leoben, Austria
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Abstract

In this paper we are concerned with the asymptotic description of the sum of digits function of canonical number systems in number fields. We derive an asymptotic formula for its summatory function whose second term contains a periodic fluctuation. In imaginary quadratic fields this function is uniformly distributed with respect to the argument.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 1 , January 1998 , pp. 37 - 45
Copyright
© The London Mathematical Society 1998

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