Diophantine inequality involving binary forms

Boqing XUE

Front. Math. China ›› 2014, Vol. 9 ›› Issue (3) : 641 -657.

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Front. Math. China ›› 2014, Vol. 9 ›› Issue (3) : 641 -657. DOI: 10.1007/s11464-013-0334-6
RESEARCH ARTICLE
RESEARCH ARTICLE

Diophantine inequality involving binary forms

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Abstract

Let r= 2d-1 + 1. We investigate the diophantine inequality

|i=1rλiΦi(xi,yi)+η||<(max1ir{|xi|,|yi|})-σ
where Φi(x, y) ∈Z[x, y] (1≤ir) are nondegenerate forms of degree d= 3 or 4.

Keywords

Diophantine inequality / binary form

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Boqing XUE. Diophantine inequality involving binary forms. Front. Math. China, 2014, 9(3): 641-657 DOI:10.1007/s11464-013-0334-6

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