Mellin Transforms and Asymptotics:
Digital Sums
Abstract.
Arithmetic functions related to number representation systems
exhibit various periodicity phenomena.
For instance, a well known theorem of Delange expresses the
total number of ones in the binary representations of
the first n integers
in terms of a periodic fractal function.
We show that such periodicity phenomena can be analyzed rather systematically
using classical tools from analytic number theory, namely
the Mellin-Perron formulae.
This approach yields naturally
the Fourier series involved in
the expansions of a variety of digital sums related to number representation
systems.
helmut@gauss.cam.wits.ac.za
Here are the addresses of my coauthors:
Philippe.Flajolet@inria.fr,
grabner@weyl.math.tu-graz.ac.at,
Peter.Kirschenhofer@tuwien.ac.at,
tichy@weyl.math.tu-graz.ac.at,
This paper is available in the Tex, Dvi, and PostScript format.
If you go to the homepage of
Philippe Flajolet,
you will find, amongst a lot of interesting things, a postscript version of this paper,
which includes the graphics!
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