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Uniform distribution of sequences generated by iterated polynomials

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Abstract

Given a polynomial f with integer coefficients and deg f > 1, a set of points

$$\left( {\frac{x} {{p^n }},\frac{{f(x)\bmod p^n }} {{p^n }}, \cdots ,\frac{{f^{(s - 1)} (x)\bmod p^n }} {{p^n }}} \right)$$

belonging to the s-dimensional unit hypercube is proved to have a uniform distribution as n → ∞. It is proved that this set also has a uniform distribution for a composition with an injective mapping defined by a synchronizing finite automaton.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    E. E. Lerner

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  1. E. E. Lerner
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Correspondence to E. E. Lerner.

Additional information

Original Russian Text © E.E. Lerner, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 3, pp. 284–286.

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Lerner, E.E. Uniform distribution of sequences generated by iterated polynomials. Dokl. Math. 92, 704–706 (2015). https://doi.org/10.1134/S1064562415060174

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  • DOI: https://doi.org/10.1134/S1064562415060174

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