On the correlations of mod 1

  • Niclas Technau

    Tel Aviv University, Israel
  • Nadav Yesha

    University of Haifa, Israel
On the correlations of $n^\alpha$ mod 1 cover
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A well known result in the theory of uniform distribution modulo 1 (which goes back to Fejér and Csillag) states that the fractional parts of the sequence are uniformly distributed in the unit interval whenever is not an integer. For sharpening this knowledge to local statistics, the -level correlation functions of the sequence are of fundamental importance. We prove that for each the -level correlation function is Poissonian for almost every .

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Niclas Technau, Nadav Yesha, On the correlations of mod 1. J. Eur. Math. Soc. 25 (2023), no. 10, pp. 4123–4154

DOI 10.4171/JEMS/1281