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.

Here are the addresses of my coauthors:,,,,

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!
(Back to List of Papers)