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Register a new userAutomorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals
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Authors
El Houcein El Abdalaoui
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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 $Mtoinfty$, $Htoinfty$, $H/Mto 0$.
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