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 λ1/λ2∉Fq(T) and sgn(λ1)+sgn(λ2)+sgn(λ 3)=0,then the values of the sumλ1P1+λ2P 2+λ3P3, 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 language | English |
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Pages (from-to) | 46-61 |
Number of pages | 16 |
Journal | Journal of Number Theory |
Volume | 78 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1999 Sept |
Keywords
- Diophantine inequalities
- Hardy-Littlewood method
ASJC Scopus subject areas
- Algebra and Number Theory