We study sets of recurrence, in both measurable and topological settings, for actions of (N, x) and (Q(>0), x). 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)(l)/(cn+ d)(l) : n is an element of N} are sets ofmultiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.
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