M\"obius orthogonality for q-semimultiplicative sequences
classification
🧮 math.NT
math.COmath.DS
keywords
sequencesfunctionobiussemimultiplicativeanalogousasymptoticallyclassconjecture
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We show that all $q$-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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