Diophantine Inequalities for Polynomial Rings

Chih Nung Hsu*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

2 引文 斯高帕斯(Scopus)

摘要

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)).

原文英語
頁(從 - 到)46-61
頁數16
期刊Journal of Number Theory
78
發行號1
DOIs
出版狀態已發佈 - 1999 九月

ASJC Scopus subject areas

  • 代數與數理論

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