Arbitrarily Slow Decay in the Mobius Disjointness Conjecture

We construct examples showing that the correlation in the Mobius disjointness conjecture can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of μ(n) one can put any bounded sequence such that the Cesàro mean of the corresponding sequence of absolute values does not tend to zero. This is a joint work with Amir Algom.