M\"{o}bius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers
Andrei Shubin

TL;DR
This paper proves that the M"obius function is orthogonal to the Thue-Morse sequence evaluated along Piatetski-Shapiro numbers for any exponent c between 1 and 2, extending previous results from squares.
Contribution
It extends M"obius orthogonality of Thue-Morse sequence from squares to Piatetski-Shapiro numbers for all c in (1,2).
Findings
M"obius function is orthogonal to Thue-Morse sequence along Piatetski-Shapiro numbers.
Orthogonality holds for all c in (1,2).
Results include sequences with maximum entropy.
Abstract
We show that the M\"{o}bius function is orthogonal to the Thue-Morse sequence taken along the Piatetski-Shapiro numbers for any . Previously this property was established for the subsequence along the squares . These are both examples of M\"{o}bius orthogonal sequences with maximum entropy.
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Taxonomy
TopicsAdvanced Mathematical Identities · semigroups and automata theory · Advanced Combinatorial Mathematics
