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The parity of the sum-of-digits-function of generalized Zeckendorf representations. (English) Zbl 0926.11006

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)

MSC:

11A63 Radix representation; digital problems
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11A67 Other number representations

Citations:

Zbl 0916.11049
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