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- W2553862977 abstract "We show that if $y=(y_n)_{nge 1}$ is a bounded sequence with zero average along every infinite arithmetic progression then for every $Nge 2$ there exist (unilateral or bilateral) subshifts $Sigma$ over $N$ symbols, with entropy arbitrarily close to $log N$, uncorrelated to $y$. In particular, for $y=mu$ being the Mobius function, we get that there exist subshifts as above which satisfy the assertion of Sarnak's conjecture. The existence of positive entropy systems uncorrelated to the Mobius function is claimed in Sarnak's survey cite{sarnak} (and attributed to Bourgain), however, to our knowledge no examples have ever been published. We fill in this gap and by the way we show that this has nothing to do with more advanced algebraic properties (for instance multiplicativity) of the considered sequence." @default.
- W2553862977 created "2016-11-30" @default.
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- W2553862977 date "2016-11-07" @default.
- W2553862977 modified "2023-09-27" @default.
- W2553862977 title "Almost full entropy subshifts uncorrelated to the Mobius function" @default.
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- W2553862977 hasPublicationYear "2016" @default.
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