Drmota, Michael; Gajdosik, Johannes The parity of the sum-of-digits-function of generalized Zeckendorf representations. (English) Zbl 0926.11006 Fibonacci Q. 36, No. 1, 3-19 (1998). The authors investigate arithmetic properties of digital expansions. In the first part they introduce a Möbius function for digital expansions and establish some basic properties of this function. In the second part of the paper the authors consider digital expansions of positive integers with respect to linear recurring sequences. They consider digital sums \[ S_G(N)= \sum_{n=0}^N (-1)^{s_G(n)}, \] where \(s_G(n)\) denotes the sum of digit function (for the number system \(G\)). Under some additional assumptions on the number system \(G\) various distribution properties of \(S_G(N)\) are established. The proofs are based on quite involved analytic tools. Reviewer: R.F.Tichy (Graz) Cited in 5 Documents MSC: 11A63 Radix representation; digital problems 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11A67 Other number representations Keywords:Möbius function; digital expansions; linear recurring sequences; digital sums; sum of digit function Citations:Zbl 0916.11049 PDFBibTeX XMLCite \textit{M. Drmota} and \textit{J. Gajdosik}, Fibonacci Q. 36, No. 1, 3--19 (1998; Zbl 0926.11006)