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A vast class of exponential functions is showed to be deterministic. This class includes functions whose exponents are polynomial-like or piece-wise close to polynomials after differentiation. Many of these functions are indeed disjoint from the Mobius function. As a consequence, we show that Sarnaks Disjointness Conjecture for the Mobius function (from deterministic sequences) is equivalent to the disjointness in average over short intervals
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.
A sequential dynamical system (SDS) consists of a graph, a set of local functions and an update schedule. A linear sequential dynamical system is an SDS whose local functions are linear. In this paper, we derive an explicit closed formula for any lin
We obtain an estimate for the average value of the product of the Mobius function and any polynomial phase over short intervals and arithmetic progressions simultaneously. As a consequence, we prove that the product of M{o}bius and any polynomial pha
We establish cancellation in short sums of certain special trace functions over $mathbb{F}_q[u]$ below the P{o}lya-Vinogradov range, with savings approaching square-root cancellation as $q$ grows. This is used to resolve the $mathbb{F}_q[u]$-analog o
We study the topological properties of Peierls transitions in a monovalent M{o}bius ladder. Along the transverse and longitudinal directions of the ladder, there exist plenty Peierls phases corresponding to various dimerization patterns. Resulted fro