Diophantine Inequalities for Polynomial Rings

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2 Citations (Scopus)

Abstract

We study the Hardy-Littlewood method for the Laurent series field Fq((1/T)) over the finite field Fq with q elements. We show that if λ1, λ2, λ3 are non-zero elements in Fq((1/T)) satisfying λ12∉Fq(T) and sgn(λ1)+sgn(λ2)+sgn(λ 3)=0,then the values of the sumλ1P12P 23P3, as Pi (i=1, 2, 3) run independently through all monic irreducible polynomials in Fq[T], are everywhere dense on the "non-Archimedean" line Fq((1/T)), where sgn(f)∈Fq denotes the leading coefficient of f∈Fq((1/T)).

Original languageEnglish
Pages (from-to)46-61
Number of pages16
JournalJournal of Number Theory
Volume78
Issue number1
DOIs
Publication statusPublished - 1999 Sep 1

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Keywords

  • Diophantine inequalities
  • Hardy-Littlewood method

ASJC Scopus subject areas

  • Algebra and Number Theory

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