Almost Full Entropy Subshifts Uncorrelated to the Möbius Function
Almost Full Entropy Subshifts Uncorrelated to the Möbius Function
We show that if |$y=(y_n)_{n\ge 1}$| is a bounded sequence with zero average along every infinite arithmetic progression then for every |$N\ge 2$| 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 Möbius …