M\"obius orthogonality for the Zeckendorf sum-of-digits function
Abstract
We show that the (morphic) sequence (-1)s(n) is asymptotically orthogonal to all bounded multiplicative functions, where s denotes the Zeckendorf sum-of-digits function. In particular we have Σn<N (-1)s(n) μ(n) = o(N), that is, this sequence satisfies the Sarnak conjecture.
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