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On the pair correlation for fractional parts of vector sequences

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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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Authors and Affiliations

  1. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, U.K. and¶ Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania, fboca@stoilow.imar.ro;¶ Current address: Department of Mathematics, University of Illinois-Urbana Champaign, 1409 West Green Street, Urbana, IL 61801, USA, fboca@math.uiuc.edu, , , , , , US

    F. P. Boca

  2. Institute for Advanced Study, School of Mathematics, Olden Lane, Princeton, NJ 08540, USA and¶ Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania;¶ Current address: Department of Mathematics, University of Illinois-Urbana Champaign, 1409 West Green Street, Urbana, IL 61801, USA, zaharesc@math.uiuc.edu, , , , , , US

    A. Zaharescu

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  1. F. P. Boca
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  2. A. Zaharescu
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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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  • DOI: https://doi.org/10.1007/PL00000523

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