Paper detail

Equidistribution results for sequences of polynomials

Let $(f_n)_{n=1}^{\infty}$ be a sequence of polynomials and $α>1$. In this paper we study the distribution of the sequence $(f_n(α))_{n=1}^{\infty}$ modulo one. We give sufficient conditions for a sequence $(f_n)_{n=1}^{\infty}$ to ensure that for Lebesgue almost every $α>1$ the sequence $(f_n(α))_{n=1}^{\infty}$ has Poissonian pair correlations. In particular, this result implies that for Lebesgue almost every $α>1$, for any $k\geq 2$ the sequence $(α^{n^k})_{n=1}^{\infty}$ has Poissonian pair correlations.