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...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/1357859 |
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| author | Wiem Gadri |
| author_facet | Wiem Gadri |
| author_sort | Wiem Gadri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4354542e3e674fbab4d269a54153663f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4354542e3e674fbab4d269a54153663f2025-02-03T01:20:50ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/13578591357859Equidistribution Modulo 1Wiem Gadri0Faculty of Science, Northern Border University, Arar, Saudi ArabiaThe 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.http://dx.doi.org/10.1155/2021/1357859 |
| spellingShingle | Wiem Gadri Equidistribution Modulo 1 Journal of Mathematics |
| title | Equidistribution Modulo 1 |
| title_full | Equidistribution Modulo 1 |
| title_fullStr | Equidistribution Modulo 1 |
| title_full_unstemmed | Equidistribution Modulo 1 |
| title_short | Equidistribution Modulo 1 |
| title_sort | equidistribution modulo 1 |
| url | http://dx.doi.org/10.1155/2021/1357859 |
| work_keys_str_mv | AT wiemgadri equidistributionmodulo1 |