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
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.
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Sbornik: Mathematics, 2001, 192:2, 261–276
MSC: Primary 11K06; Secondary 11J71
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
\paper Probability and ergodic laws in the distribution of the~fractional parts of the~values of polynomials
\jour Mat. Sb.
\jour Sb. Math.
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This publication is cited in the following articles:
L. D. Pustyl'nikov, “Generalized continued fractions and ergodic theory”, Russian Math. Surveys, 58:1 (2003), 109–159
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