A higher-dimensional Kurzweil theorem for formal Laurent series over finite fields

Shu Yi Chen; Michael Fuchs

doi:10.1016/j.ffa.2012.08.001

A higher-dimensional Kurzweil theorem for formal Laurent series over finite fields

Shu Yi Chen, Michael Fuchs^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In a recent paper, Kim and Nakada proved an analogue of Kurzweils theorem for inhomogeneous Diophantine approximation of formal Laurent series over finite fields. Their proof used continued fraction theory and thus cannot be easily extended to simultaneous Diophantine approximation. In this note, we give another proof which works for simultaneous Diophantine approximation as well.

Original language	English
Pages (from-to)	1195-1206
Number of pages	12
Journal	Finite Fields and their Applications
Volume	18
Issue number	6
DOIs	https://doi.org/10.1016/j.ffa.2012.08.001
State	Published - Nov 2012

Keywords

Formal Laurent series
Inhomogeneous Diophantine approximation
Kurzweils theorem
Simultaneous Diophantine approximation

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10.1016/j.ffa.2012.08.001

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title = "A higher-dimensional Kurzweil theorem for formal Laurent series over finite fields",

abstract = "In a recent paper, Kim and Nakada proved an analogue of Kurzweils theorem for inhomogeneous Diophantine approximation of formal Laurent series over finite fields. Their proof used continued fraction theory and thus cannot be easily extended to simultaneous Diophantine approximation. In this note, we give another proof which works for simultaneous Diophantine approximation as well.",

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AB - In a recent paper, Kim and Nakada proved an analogue of Kurzweils theorem for inhomogeneous Diophantine approximation of formal Laurent series over finite fields. Their proof used continued fraction theory and thus cannot be easily extended to simultaneous Diophantine approximation. In this note, we give another proof which works for simultaneous Diophantine approximation as well.

KW - Formal Laurent series

KW - Inhomogeneous Diophantine approximation

KW - Kurzweils theorem

KW - Simultaneous Diophantine approximation

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ER -

A higher-dimensional Kurzweil theorem for formal Laurent series over finite fields

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Keywords

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