A refined Kurzweil type theorem in positive characteristic

Dong Han Kim, Hitoshi Nakada, Rie Natsui

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a Kurzweil type inhomogeneous Diophantine approximation theorem in the field of the formal Laurent series for a monotone sequence of approximation. We find a necessary and sufficient condition for irrational f and monotone increasing (ℓn) that there are infinitely many polynomials P and Q such that |Qf-P-g|<q-n-ℓn, n=deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (ℓn) with Σq- ℓn=∞ there are infinitely many solutions for almost every g.

Original languageEnglish
Pages (from-to)64-75
Number of pages12
JournalFinite Fields and Their Applications
Volume20
Issue number1
DOIs
Publication statusPublished - 2013 Mar

Fingerprint

Positive Characteristic
Monotone
Polynomials
Monotone Sequences
Laurent Series
Infinitely Many Solutions
Diophantine Approximation
Approximation Theorem
Theorem
Necessary Conditions
Polynomial
Sufficient Conditions
Approximation

Keywords

  • Formal Laurent series
  • Inhomogeneous Diophantine approximation
  • Kurzweil type theorem

ASJC Scopus subject areas

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

Cite this

A refined Kurzweil type theorem in positive characteristic. / Kim, Dong Han; Nakada, Hitoshi; Natsui, Rie.

In: Finite Fields and Their Applications, Vol. 20, No. 1, 03.2013, p. 64-75.

Research output: Contribution to journalArticle

Kim, Dong Han ; Nakada, Hitoshi ; Natsui, Rie. / A refined Kurzweil type theorem in positive characteristic. In: Finite Fields and Their Applications. 2013 ; Vol. 20, No. 1. pp. 64-75.
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