On a property of non liouville numbers

Abstract

Let α be a non Liouville number and let f(x) = αxr + ar−1xr−1 + ··· + a1x+a0 ϵ R[x] be a polynomial of positive degree r. We consider the sequence (yn)n≥1 defined by yn = f(h(n)), where h belongs to a certain family of arithmetic functions and show that (yn)n≥1 is uniformly distributed modulo 1.