ON THE PROBLEM OF INTEGER SOLUTIONS TO DECOMPOSABLE FORM INEQUALITIES
ON THE PROBLEM OF INTEGER SOLUTIONS TO DECOMPOSABLE FORM INEQUALITIES
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DOI：
10.1142/s1793042108001766
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发表时间：
2008-10
影响因子：
0.7
通讯作者：
Yuancheng Liu
中科院分区：
文献类型：
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作者：
Yuancheng Liu
本文证明了Chen和Ru在文[1]中提出的关于可分解形式不等式整数解个数有限性的一个猜想。设k是数域，F（X1，…，Xm）是系数在k中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 0，该不等式只有n n个非比例解，其中HS（x1，.，xm）= n n ∈ Smax 1 ≤i≤m||习||是S高度。
This paper proves a conjecture proposed by Chen and Ru in [1] 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 show that for every finite set of places S of k containing the archimedean places of k, for each real number λ 0, the inequality has only finitely many -non-proportional solutions, where HS(x1,…,xm) = Πυ∈Smax1≤i≤m ||xi||υ is the S-height.