### Abstract

We consider a Kurzweil type inhomogeneous Diophantine approximation theorem in the field of the formal Laurent series for a monotone sequence of approximation. We find a necessary and sufficient condition for irrational f and monotone increasing (^{ℓn}) that there are infinitely many polynomials P and Q such that |Qf-P-g|<q-^{n}-^{ℓn}, n=deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (^{ℓn}) with Σq- ^{ℓn}=∞ there are infinitely many solutions for almost every g.

Original language | English |
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Pages (from-to) | 64-75 |

Number of pages | 12 |

Journal | Finite Fields and their Applications |

Volume | 20 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Mar 1 |

### Keywords

- Formal Laurent series
- Inhomogeneous Diophantine approximation
- Kurzweil type theorem

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Engineering(all)
- Applied Mathematics

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## Cite this

Kim, D. H., Nakada, H., & Natsui, R. (2013). A refined Kurzweil type theorem in positive characteristic.

*Finite Fields and their Applications*,*20*(1), 64-75. https://doi.org/10.1016/j.ffa.2012.12.002