On the pair correlation for fractional parts of vector sequences

Abstract.

We study the pair correlation for fractional parts of vector sequences and provide a sufficient condition for being poissonian. As a consequence, a large class of sequences of fractional parts of integer polynomials in several variables, lacunary integer sequences and linear combinations between them are shown to have poissonian pair correlation.

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Eingegangen am 21. 2. 2000

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Boca, F., Zaharescu, A. On the pair correlation for fractional parts of vector sequences. Arch. Math. 77, 498–507 (2001). https://doi.org/10.1007/PL00000523

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Keywords

  • Linear Combination
  • Large Class
  • Pair Correlation
  • Fractional Part
  • Vector Sequence