Donoso, SebastianLe, Ahn N.Moreira, JoelSun, Wenbo2024-01-242024-01-242023-04-010021-7670https://hdl.handle.net/10919/117641We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ>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) ℓ: n ∈ ℕ} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.Pages 719-761application/pdfenIn CopyrightArticle - Refereedhttps://doi.org/10.1007/s11854-022-0264-x1492Sun, Wenbo [0000-0003-3399-3937]1565-8538