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We show that Sarnaks conjecture on Mobius disjointness holds in every uniquely ergodic modelof a quasi-discrete spectrum automorphism. A consequence of this result is that, for each non constant polynomial $PinR[x]$ with irrational leading coefficient and for each multiplicative function $bnu:NtoC$, $|bnu|leq1$, we have[ frac{1}{M} sum_{Mle mtextless{}2M} frac{1}{H} left| sum_{mle n textless{} m+H} e^{2pi iP(n)}bnu(n) right|longrightarrow 0 ] as $Mtoinfty$, $Htoinfty$, $H/Mto 0$.
In this paper, we study dynamics of maps on quasi-graphs characterizing their invariant measures. In particular, we prove that every invariant measure of quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we obtain an
It is shown that in a class of counterexamples to Elliotts conjecture by Matomaki, Radziwill and Tao, the Chowla conjecture holds along a subsequence.
We provide a criterion for a point satisfying the required disjointness condition in Sarnaks Mobius Disjointness Conjecture. As a direct application, we have that the conjecture holds for any topological model of an ergodic system with discrete spectrum.
We study sets of recurrence, in both measurable and topological settings, for actions of $(mathbb{N},times)$ and $(mathbb{Q}^{>0},times)$. In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems
We study the spectral disjointness of the powers of a rank-one transformation. For a large class of rank-one constructions, including those for which the cutting and stacking parameters are bounded, and other examples such as rigid generalized Chacon