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

Eveyth Deligero, Michael Fuchs, Hitoshi Nakada

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)535-545
Number of pages11
JournalFinite Fields and Their Applications
Volume13
Issue number3
DOIs
Publication statusPublished - 2007 Jul

Fingerprint

Laurent Series
Diophantine Approximation
Invariance Principle
Invariance
Functional Law of the Iterated Logarithm
Functional Central Limit Theorem
Coprime
Approximation Problem
Theorem
Central limit theorem
Refinement

Keywords

  • Diophantine approximation
  • Formal Laurent series
  • Invariance principles

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Invariance principles for Diophantine approximation of formal Laurent series over a finite base field. / Deligero, Eveyth; Fuchs, Michael; Nakada, Hitoshi.

In: Finite Fields and Their Applications, Vol. 13, No. 3, 07.2007, p. 535-545.

Research output: Contribution to journalArticle

Deligero, Eveyth ; Fuchs, Michael ; Nakada, Hitoshi. / Invariance principles for Diophantine approximation of formal Laurent series over a finite base field. In: Finite Fields and Their Applications. 2007 ; Vol. 13, No. 3. pp. 535-545.
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