Browsing by Author "Donoso, Sebastian"
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- Additive averages of multiplicative correlation sequences and applicationsDonoso, 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.
- Averages of completely multiplicative functions over the Gaussian integersDonoso, Sebastian; Le, Anh; Moreira, Joel; Sun, Wenbo (2024)
- Joint ergodicity for functions of polynomial growthWe provide necessary and sufficient conditions for joint ergodicity results for systems of commuting measure preserving transformations for an iterated Hardy field function of polynomial growth. Our method builds on and improves recent techniques due to Frantzikinakis and Tsinas, who dealt with multiple ergodic averages along Hardy field functions; it also enhances an approach introduced by the authors and Ferré Moragues to study polynomial iterates.