Mellin Transforms and Asymptotics:
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
Here are the addresses of my coauthors:
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