论文标题
同时进行双苯胺近似的定理
Going-up theorems for simultaneous Diophantine approximation
论文作者
论文摘要
我们建立了几个新的不等式，将与真实矢量$ \ usevector $ \ usewisemence相关的经典指数链接了二元近似的经典指数，之一因此，我们获得了Badziahin和Bugeaud的最新结果的变体和部分改进。我们进一步隐含地恢复了Bugeaud和Laurent的不平等现象，并提供了新的证据。关于$ \ mathbb {q} $ - 线性独立坐标的一般真实向量（不在Veronese曲线）的类似估计值也被解决。我们的方法基于Minkowski的第二个凸体定理，该定理应用于Schmidt和Summerer引入的数字的参数几何框架中。我们还经常在极地凸体上使用Mahler的双重性结果。
We establish several new inequalities linking classical exponents of Diophantine approximation associated to a real vector $\underlineξ=(ξ,ξ^{2},\ldots,ξ^{N})$, in various dimensions $N$. We thereby obtain variants, and partly refinements, of recent results of Badziahin and Bugeaud. We further implicitly recover inequalities of Bugeaud and Laurent as special cases, with new proofs. Similar estimates concerning general real vectors (not on the Veronese curve) with $\mathbb{Q}$-linearly independent coordinates are addressed as well. Our method is based on Minkowski's Second Convex Body Theorem, applied in the framework of parametric geometry of numbers introduced by Schmidt and Summerer. We also frequently employ Mahler's Duality result on polar convex bodies.
