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 nαn∈N where 0<α<1, is the study of the sequence K1/l, where K is a polynomial having an l-th root in the fie...

Full description

Bibliographic Details
Main Author: Wiem Gadri
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/1357859
Description
Summary: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 nαn∈N where 0<α<1, is the study of the sequence K1/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.
ISSN:2314-4785