Abstract

We study sets of recurrence, in both measurable and topological settings, for actions of (?, ×) and (?>0, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(an+b)1/(cn+d) ?: n ? ?} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function. © 2023, The Hebrew University of Jerusalem.