Equidistribution Modulo 1. (19th February 2021) - Gadri, Wiem
Abstract : 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.