Invariance principles for Diophantine approximation of formal Laurent series over a finite base field

Eveyth Deligero, Michael Fuchs, Hitoshi Nakada

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)535-545
ページ数11
ジャーナルFinite Fields and their Applications
13
3
DOI
出版ステータスPublished - 2007 7月
外部発表はい

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 代数と数論
  • 工学(全般)
  • 応用数学

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