Möbius orthogonality for the Zeckendorf sum-of-digits function

Michael Drmota; Clemens Müllner; Lukas Spiegelhofer

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arXiv · 1706.09680

Möbius orthogonality for the Zeckendorf sum-of-digits function

Michael Drmota·Clemens Müllner·Lukas Spiegelhofer

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Abstract

We show that the (morphic) sequence $(-1)^{s_φ(n)}$ is asymptotically orthogonal to all bounded multiplicative functions, where $s_φ$ denotes the Zeckendorf sum-of-digits function. In particular we have $\sum_{n<N} (-1)^{s_φ(n)} μ(n) = o(N)$, that is, this sequence satisfies the Sarnak conjecture.

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BibTeX RIS

Michael Drmota, Clemens Müllner, Lukas Spiegelhofer. 2017-06-29. Möbius orthogonality for the Zeckendorf sum-of-digits function. https://arxiv.org/abs/1706.09680

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