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Mat. Sb., 2001, Volume 192, Number 2, Pages 103–118 (Mi msb545)  

This article is cited in 1 scientific paper (total in 1 paper)

Probability and ergodic laws in the distribution of the fractional parts of the values of polynomials

L. D. Pustyl'nikov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: In the present paper the fractional parts of the values of a polynomial are regarded as random variables depending on a randomly chosen vector whose coordinates are all the coefficients of the polynomial except the leading coefficient, which is assumed to be fixed. It is proved that the fractional parts and the distances between them are equally distributed and independent; the strong and superstrong laws of large numbers and the central limit theorem are proved for them. The probability distribution is found for the fractional part of a sum of the values of polynomials, which turns out to be universal.

DOI: https://doi.org/10.4213/sm545

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English version:
Sbornik: Mathematics, 2001, 192:2, 261–276

Bibliographic databases:

UDC: 511.36
MSC: Primary 11K06; Secondary 11J71
Received: 28.12.1999

Citation: L. D. Pustyl'nikov, “Probability and ergodic laws in the distribution of the fractional parts of the values of polynomials”, Mat. Sb., 192:2 (2001), 103–118; Sb. Math., 192:2 (2001), 261–276

Citation in format AMSBIB
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\by L.~D.~Pustyl'nikov
\paper Probability and ergodic laws in the distribution of the~fractional parts of the~values of polynomials
\jour Mat. Sb.
\yr 2001
\vol 192
\issue 2
\pages 103--118
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\crossref{https://doi.org/10.4213/sm545}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1835988}
\zmath{https://zbmath.org/?q=an:1022.37008}
\transl
\jour Sb. Math.
\yr 2001
\vol 192
\issue 2
\pages 261--276
\crossref{https://doi.org/10.1070/sm2001v192n02ABEH000545}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0035605727}


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  • https://doi.org/10.4213/sm545
  • http://mi.mathnet.ru/eng/msb/v192/i2/p103

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. D. Pustyl'nikov, “Generalized continued fractions and ergodic theory”, Russian Math. Surveys, 58:1 (2003), 109–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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