Equidistribution results for sequences of polynomials.

Let (f n) n = 1 ∞ be a sequence of polynomials and α > 1. In this paper we study the distribution of the sequence (f n (α)) n = 1 ∞ modulo one. We give sufficient conditions for a sequence (f n) n = 1 ∞ to ensure that for Lebesgue almost every α > 1 the sequence (f n (α)) n = 1 ∞ has Poissonian pair correlations. In particular, this result implies that for Lebesgue almost every α > 1 , for any k ≥ 2 the sequence (α n k ) n = 1 ∞ has Poissonian pair correlations. [ABSTRACT FROM AUTHOR]