Diophantine Inequalities for Polynomial Rings

Chih Nung Hsu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number1
Publication statusPublished - 1999 Sept


  • Diophantine inequalities
  • Hardy-Littlewood method

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Diophantine Inequalities for Polynomial Rings'. Together they form a unique fingerprint.

Cite this