M\"obius orthogonality for $q$-semimultiplicative sequences
Jakub Konieczny
TL;DR
This paper proves that all q-semimultiplicative sequences are orthogonal to the Möbius function, confirming the Sarnak conjecture for this class and extending previous results on digital sequences.
Contribution
It establishes the Sarnak conjecture for q-semimultiplicative sequences, generalizing prior results on sum-of-digits and digital sequences.
Findings
q-semimultiplicative sequences are orthogonal to the Möbius function
Confirms the Sarnak conjecture for this class
Extends results from digital sequences to a broader class
Abstract
We show that all -semimultiplicative sequences are asymptotically orthogonal to the M\"obius function, thus proving the Sarnak conjecture for this class of sequences. This generalises analogous results for the sum-of-digits function and other digital sequences which follow from previous work of Mauduit and Rivat.
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