论文标题
关于vojta的算法，具有截短的计数功能
On the arithmetic case of Vojta's conjecture with truncated counting functions
论文作者
论文摘要
我们证明，在VOJTA的猜想的方向上，有合理点的二聚体近似不等式，并具有截短的计数函数。我们的结果还为$ abc $猜想提供了一个界限，在某些情况下是次指数的。主定理给出了相对于代数点的近距离，相对于具有足够多组分的除数的截短计数函数给出了一个下限。此外，我们表明Lang-Waldschmidt的猜想意味着vojta的猜想的特殊情况，并在任意维度中截断。我们的方法基于对数中线性形式的理论和几何结构。
We prove a Diophantine approximation inequality for rational points in varieties of any dimension, in the direction of Vojta's conjecture with truncated counting functions. Our results also provide a bound towards the $abc$ conjecture which in several cases is subexponential. The main theorem gives a lower bound for the truncated counting function relative to a divisor with sufficiently many components, in terms of the proximity to an algebraic point. Furthermore, we show that the Lang-Waldschmidt conjecture implies a special case of Vojta's conjecture with truncation in arbitrary dimension. Our methods are based on the theory of linear forms in logarithms and a geometric construction.
