Probabilistic and Ergodic Laws in the Distribution of Fractional Parts of the Polynomials Values

In this work fractional parts of a polynomial are considered as random variables depending on a random vector with coordinates which are all coefficients of the polynomial except the leading coefficient which is proposed to be fixed. There are proved the same distribution, independence, strong and the most strong laws of large numbers for fractional parts and for distances between them and the central limit theorem. It is found the distribution of probability of the fractional part of a sum of polynomial values, which it turns out to be universal.