• Corpus ID: 235485265

Pair Correlation of the Fractional Parts of $\alpha n^\theta$

@inproceedings{Lutsko2021PairCO,
  title={Pair Correlation of the Fractional Parts of \$\alpha n^\theta\$},
  author={Christopher Lutsko and Athanasios Sourmelidis and Niclas Technau},
  year={2021}
}
Fix α, θ > 0, and consider the sequence (αn mod 1)n≥1. Since the seminal work of Rudnick– Sarnak (1998), and due to the Berry–Tabor conjecture in quantum chaos, the fine-scale properties of these dilated mononomial sequences have been intensively studied. In this paper we show that for θ ≤ 1/3, and α > 0, the pair correlation function is Poissonian. While (for a given θ 6= 1) this strong pseudo-randomness property has been proven for almost all values of α, there are next-to-no instances where… 

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