Equidistribution modulo 1 (Q2034929)

Summary: The generalisation of questions of the classic arithmetic has long been of interest. One line of questioning, introduced by \textit{M. Car} [Acta Arith. 88, No. 2, 141--153 (1999; Zbl 0947.11036)], inspired by the equidistribution of the sequence \((n^\alpha)_{n\in N}\) where \(0<\alpha<1\), 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 \(L'\equiv B\mod C\). Our main result is to prove the uniform distribution in the Laurent series case. Particularly, we prove the case for irreducible polynomials.