Equidistribution results for sequences of polynomials

Let (fn)^∞_n=1 be a sequence of polynomials and α >1. In this paper we study the distribution of the sequence (fn(α))^∞_n=1 modulo one. We give sufficient conditions for a sequence (fn)^∞_n=1to ensure that for Lebesgue almost every α >1the sequence (fn(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 (αnk)^∞_n=1 has Poissonian pair correlations.