MELLIN TRANSFORMS AND ASYMPTOTICS - DIGITAL SUMS

Arithmetic functions related to number representation systems exhibit various periodicity phenomena. For instance, a well-known theorem of D elange expresses the total number of ones in the binary representation s of the first n integers in terms of a periodic fractal function. We show that such periodicity phenomena can be analyzed rather systematic ally using classical tools from analytic number theory, namely the Mel lin-Perron formulae. This approach yields naturally the Fourier series involved in the expansions of a variety of digital sums related to nu mber representation systems.