On the pair correlation for fractional parts of vector sequences

Archiv der Mathematik volume 77, pages498–507(2001)Cite this article

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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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

Authors
  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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Keywords

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