Browsing by Author "Moreira, Joel"

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    Additive averages of multiplicative correlation sequences and applications
    Donoso, Sebastian; Le, Ahn N.; Moreira, Joel; Sun, Wenbo (Springer, 2023-04-01)
    We 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.
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    Averages of completely multiplicative functions over the Gaussian integers
    Donoso, Sebastian; Le, Anh; Moreira, Joel; Sun, Wenbo (2024)