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

作者：el Abdalaoui El Houcein; Lemanczyk Mariusz; de la Rue Thierry^*

来源：International Mathematics Research Notices, 2017, (14): 4350-4368.

DOI：10.1093/imrn/rnw146

We show that Sarnak's conjecture on Mobius 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 is an element of R[x] with irrational leading coefficient and for each multiplicative function. upsilon: N -> C, vertical bar upsilon vertical bar <= 1, we have
1/M Sigma(M <= m < 2M) 1/H vertical bar Sigma(m <= n < m+H) e(2 pi ip(n)) upsilon(n)vertical bar -> 0
as M -> infinity, H -> infinity, H/M -> 0.

• 出版日期2017-7