| MSC: | 11A63 | Radix representation; digital problems |
| 26A30 | Singular functions, Cantor functions, functions with other special properties | |
| 39B22 | Equations for real functions | |
| ZDM: | - | |
| CR: | - | |
| PACS: | - |
Abstract:
In this paper we show connections between sums related to the binary sum-
of-digits function and the function of de Rham Ra (x), and its partial derivatives with respect
to the parameter. Starting point is a formula from [3] for the calculation of Ra (x) for dyadic
rational x. From this we derive an exact formula for exponential sums of digital sums, and by
means of usual differentiations we find exact expressions for some digital sums. In particular,
we get the well known result of Trollope-Delange concerning the sum-of-digits function and
the formula of Coquet for power sums of digital sums.