Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators

V. Berthé, H. Nakada, R. Natsui

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the strong law of large numbers for the number of solutions of the inequalities under consideration.

Original languageEnglish
Pages (from-to)849-866
Number of pages18
JournalFinite Fields and Their Applications
Volume14
Issue number4
DOIs
Publication statusPublished - 2008 Nov

Fingerprint

Diophantine Approximation
Number of Solutions
Denominator
Asymptotic Behavior
Irreducible polynomial
Rational functions
Strong law of large numbers
Formal Power Series
Rational function
Galois field
Polynomials
Metric
Coefficient
Approximation

Keywords

  • Laurent formal power series
  • Metric Diophantine approximation
  • Strong law of large numbers

ASJC Scopus subject areas

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

Cite this

Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators. / Berthé, V.; Nakada, H.; Natsui, R.

In: Finite Fields and Their Applications, Vol. 14, No. 4, 11.2008, p. 849-866.

Research output: Contribution to journalArticle

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