Equidistribution results for sequences of polynomials

Abstract 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.