THE SUM-OF-DIGITS FUNCTION FOR COMPLEX BASES

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 functio...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 1998-02, Vol.57 (1), p.20-40
Main Authors: GRABNER, PETER J., KIRSCHENHOFER, PETER, PRODINGER, HELMUT
Format: Article
Language:English
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Summary: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.
ISSN:0024-6107
1469-7750
DOI:10.1112/S0024610798005663