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PreprintCC BY 4.0arXiv

Metric Poissonian Pair Correlation Property Part 1: The Case n+log n

Abstract

We prove that (α(n+log n))n≥1 has Poissonian pair correlation for Lebesgue almost every real α. This solves a Problem posed by Aistleitner, El-Baz and Munsch [Open Problem 2, Geom. Funct. Anal. 2021].

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BibTeX
@misc{tan2026metric,
  title = {{Metric Poissonian Pair Correlation Property Part 1: The Case \(n+\log n\)}},
  author = {Bo Tan and Zhen Zhang and Qing-Long Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22836},
  eprint = {2610.22836},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22836},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Metric Poissonian Pair Correlation Property Part 1: The Case n+log n
AU  - Bo Tan
AU  - Zhen Zhang
AU  - Qing-Long Zhou
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.22836
UR  - https://arxiv.org/abs/2610.22836
AB  - We prove that (α(n+log n))_n≥1 has Poissonian pair correlation for Lebesgue almost every real α. This solves a Problem posed by Aistleitner, El-Baz and Munsch [Open Problem 2, Geom. Funct. Anal. 2021].
ER  -