M\"obius Disjointness for Nilsequences Along Short Intervals
Xiaoguang He, Zhiren Wang

TL;DR
This paper establishes bounds on the decay of short interval correlations between the Möbius function and nilsequences, demonstrating a form of Möbius disjointness along short intervals on nilmanifolds.
Contribution
It proves a uniform decay bound for short interval averages of Möbius and nilsequence correlations, extending Möbius disjointness results to short intervals on nilmanifolds.
Findings
Bound on short interval correlation decay as H,N grow
Uniformity of bounds across nilmanifold elements and functions
Extension of Möbius disjointness to short intervals
Abstract
For a nilmanifold , a -Lipschitz continuous function and the M\"obius sequence , we prove a bound on the decay of the averaged short interval correlation as . The bound is uniform in , and .
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Mathematical Dynamics and Fractals
