On the central limit theorem for non-archimedean diophantine approximations

Eveyth Deligero, Hitoshi Nakada

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a Diophantine inequality: [InlineMediaObject not available: see fulltext.] on the set of formal Laurent series of negative degree. We show that under these two conditions: (i) q n Ψ(n) is a monotone non-increasing and (ii) ∑n q n Ψ(n)=∞, a central limit theorem holds for the number of solutions. The proof is based on the construction of a non-stationary one dependent process associated with the Diophantine inequality.

Original languageEnglish
Pages (from-to)51-64
Number of pages14
JournalManuscripta Mathematica
Volume117
Issue number1
DOIs
Publication statusPublished - 2005 May

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Diophantine Inequalities
Diophantine Approximation
Central limit theorem
Laurent Series
Number of Solutions
Monotone
Dependent

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the central limit theorem for non-archimedean diophantine approximations. / Deligero, Eveyth; Nakada, Hitoshi.

In: Manuscripta Mathematica, Vol. 117, No. 1, 05.2005, p. 51-64.

Research output: Contribution to journalArticle

Deligero, Eveyth ; Nakada, Hitoshi. / On the central limit theorem for non-archimedean diophantine approximations. In: Manuscripta Mathematica. 2005 ; Vol. 117, No. 1. pp. 51-64.
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