Automorphisms with Quasi-discrete Spectrum, Multiplicative Functions and Average Orthogonality Along Short Intervals

Abstract

We show that Sarnak's conjecture on Mbius disjointness holds in every uniquely ergodic model of a quasi-discrete spectrum automorphism. A consequence of this result is that, for each non constant polynomial P R[x] with irrational leading coefficient and for each multiplicative function : N C, || 1, we have