Integer solutions to decomposable form inequalities
Integer solutions to decomposable form inequalities
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DOI：
10.1016/j.jnt.2004.10.004
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发表时间：
2005-11
影响因子：
0.7
通讯作者：
Zhihua Chen;M. Ru
中科院分区：
文献类型：
--
作者：
Zhihua Chen;M. Ru
本文得到了可分解形式不等式整数解个数有限的一个结果。设k为数域，设F（X1，...，Xm）是系数为k的非退化可分解形式。证明了对k的包含k的阿基米德位置的有限位置集S，对每个真实的数λ <1m-1 and for each constant c>0，不等式只有1/2个OS*-非比例解.
This paper obtains a result on the finiteness of the number of integer solutions to decomposable form inequalities. Let k be a number field and let F(X1,...,Xm) be a non-degenerate decomposable form with coefficients in k. We prove that, for every finite set of places S of k containing the archimedean places of k, for each real number λ<1m-1 and for each constant c>0, the inequalityhas only finitely many OS*-non-proportional solutions.