Mellin Transforms And Asymptotics: Digital Sums (1993)
| Citations: | 32 - 11 self |
BibTeX
@MISC{Flajolet93mellintransforms,
author = {Philippe Flajolet and Peter Grabner and Peter Kirschenhofer and Helmut Prodinger and Robert F. Tichy},
title = {Mellin Transforms And Asymptotics: Digital Sums},
year = {1993}
}
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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.
