RESEARCH ARTICLE

Diophantine inequality involving binary forms

  • Boqing XUE
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  • Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received date: 16 Jul 2013

Accepted date: 24 Sep 2013

Published date: 24 Jun 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Boqing XUE . Diophantine inequality involving binary forms[J]. Frontiers of Mathematics in China, 2014 , 9(3) : 641 -657 . DOI: 10.1007/s11464-013-0334-6

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