CaltechAUTHORS
Published June 16, 2022 | Version Submitted
Journal Article Open

The metric theory of the pair correlation function for small non‐integer powers

Creators

  • 1. ROR icon Tel Aviv University
  • 2. ROR icon California Institute of Technology

Abstract

For 0 < θ < 1, we show that for almost all α, the pair correlation function of the sequence of fractional parts of {α_n^θ : n ≥ 1} is Poissonian.

Additional Information

© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. Version of Record online: 15 June 2022. Manuscript accepted: 24 April 2022. Manuscript revised: 10 April 2022. Manuscript received: 29 July 2021. The authors thank Daniel El-Baz and Shvo Regavim for insightful feedback. Zeév Rudnick was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No. 786758). Niclas Technau was supported by the Austrian Science Fund (FWF), project J 4464-N.

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Additional details

Identifiers

Eprint ID
116180
DOI
10.1112/jlms.12647
Resolver ID
CaltechAUTHORS:20220808-887235000

Related works

Describes
https://arxiv.org/abs/2107.07092 (URL)

Funding

European Research Council (ERC)
786758
FWF Der Wissenschaftsfonds
J 4464-N

Dates

Created
2022-08-09
Created from EPrint's datestamp field
Updated
2023-07-06
Created from EPrint's last_modified field