### Abstract

In a recent paper, the first and third author proved a central limit theorem for the number of coprime solutions of the Diophantine approximation problem for formal Laurent series in the setting of the classical theorem of Khintchine. In this note, we consider a more general setting and show that even an invariance principle holds, thereby improving upon earlier work of the second author. Our result yields two consequences: (i) the functional central limit theorem and (ii) the functional law of the iterated logarithm. The latter is a refinement of Khintchine's theorem for formal Laurent series. Despite a lot of research efforts, the corresponding results for Diophantine approximation of real numbers have not been established yet.

Original language | English |
---|---|

Pages (from-to) | 535-545 |

Number of pages | 11 |

Journal | Finite Fields and their Applications |

Volume | 13 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Jul 1 |

### Keywords

- Diophantine approximation
- Formal Laurent series
- Invariance principles

### ASJC Scopus subject areas

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

## Fingerprint Dive into the research topics of 'Invariance principles for Diophantine approximation of formal Laurent series over a finite base field'. Together they form a unique fingerprint.

## Cite this

*Finite Fields and their Applications*,

*13*(3), 535-545. https://doi.org/10.1016/j.ffa.2006.03.004