Christoph Aistleitner

Almost sure asymptotics for the number variance of dilations of integer sequences

Let $(x_n)_{n=1}^\infty$ be a sequence of integers. We study the number variance of dilations $(αx_n)_{n=1}^\infty$ modulo 1 in intervals of length $S$, and establish pseudorandom (Poissonian) behavior for Lebesgue-almost all $α$ throughout a large range of $S$, subject to certai...