The number of solutions of decomposable form equations
The number of solutions of decomposable form equations
复制标题
可分解形式方程的解数
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
J. Evertse
中科院分区：
文献类型：
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作者：
J. Evertse
只有有限多个解决方案。Thue和Mahler的丢番图逼近技术以及Siegel，Dyson，Roth和Bombieri的改进使得得到(1.1)的解的个数的良好的显式上界成为可能。到目前为止，由于Bombieri[1]，最好的这种上界是2×(12r)(Bombieri假设F是不可约的，r≥6在他的证明中不是本质的)。对于t=0，即|F(x，y)|=1 in x，y∈Z，Bombieri和Schmidt[2]导出了以r表示的上界常数×r。
has only finitely many solutions. The Diophantine approximation techniques of Thue and Mahler and improvements by Siegel, Dyson, Roth and Bombieri made it possible to derive good explicit upper bounds for the number of solutions of (1.1). The best such upper bound to date, due to Bombieri [1] is 2× (12r) (Bombieri assumed that F is irreducible and r ≥ 6 which was not essential in his proof). For t = 0, i.e. |F (x, y)| = 1 in x, y ∈ Z, Bombieri and Schmidt [2] derived the upper bound constant×r which is best possible in terms of r.