Equidistribution Modulo 1

The generalisation of questions of the classic arithmetic has long been of interest. One line of questioning, introduced by Car in 1995, inspired by the equidistribution of the sequence n α n ∈ N where 0 < α < 1 , is the study of the sequence K 1 / l , where K is a polynomial having an l-th root in the field of formal power series. In this paper, we consider the sequence L ′ 1 / l , where L ′ is a polynomial having an l-th root in the field of formal power series and satisfying L ′ ≡ B   mod   C . Our main result is to prove the uniform distribution in the Laurent series case. Particularly, we prove the case for irreducible polynomials.