• Corpus ID: 235485265

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

  title={Pair Correlation of the Fractional Parts of \$\alpha n^\theta\$},
  author={Christopher Lutsko and Athanasios Sourmelidis and Niclas Technau},
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… 


Long-range correlations of sequences modulo 1
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  • D. R. Heath-Brown
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2010
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