Additive averages of multiplicative correlation sequences and applications
| dc.contributor.author | Donoso, Sebastian | en |
| dc.contributor.author | Le, Ahn N. | en |
| dc.contributor.author | Moreira, Joel | en |
| dc.contributor.author | Sun, Wenbo | en |
| dc.date.accessioned | 2024-01-24T14:26:14Z | en |
| dc.date.available | 2024-01-24T14:26:14Z | en |
| dc.date.issued | 2023-04-01 | en |
| dc.description.abstract | 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. | en |
| dc.description.version | Accepted version | en |
| dc.format.extent | Pages 719-761 | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | https://doi.org/10.1007/s11854-022-0264-x | en |
| dc.identifier.eissn | 1565-8538 | en |
| dc.identifier.issn | 0021-7670 | en |
| dc.identifier.issue | 2 | en |
| dc.identifier.orcid | Sun, Wenbo [0000-0003-3399-3937] | en |
| dc.identifier.uri | https://hdl.handle.net/10919/117641 | en |
| dc.identifier.volume | 149 | en |
| dc.language.iso | en | en |
| dc.publisher | Springer | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.title | Additive averages of multiplicative correlation sequences and applications | en |
| dc.title.serial | Journal d'Analyse Mathematique | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |
| dc.type.other | Journal Article | en |
| pubs.organisational-group | /Virginia Tech | en |
| pubs.organisational-group | /Virginia Tech/Science | en |
| pubs.organisational-group | /Virginia Tech/Science/Mathematics | en |
| pubs.organisational-group | /Virginia Tech/All T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Science/COS T&R Faculty | en |