论迁移原理与Nesterenko线性独立性准则
On transference principle and Nesterenko's linear independence criterion
摘要：
我们考虑实数$θ_1, \ldots,θ_n$与有理数的同时逼近问题和线性型$x_0+θ_1x_1+\ldots+θ_nx_n$的值在整数点逼近零的对偶问题。在这种情况下，我们分析了两个迁移不等式得到的施密特和Summerer。我们给出了一个相当简单的几何观察，证明了他们的结果。我们还得到了一些以前未知的推论。特别地，我们证明了Schmidt和Summerer不等式与一致指数的转移不等式一起，包含了Bugeaud和Laurent不等式以及Marnat和Moshchevitin不等式的“一半”.除此之外，我们还证明了我们的主要构造为Nesterenko的线性独立性准则提供了一个相当简单的证明。
英文摘要：
We consider the problem of simultaneous approximation of real numbers $θ_1, \ldots,θ_n$ with rationals and the dual problem of approximating zero with the values of the linear form $x_0+θ_1x_1+\ldots+θ_nx_n$ at integer points. In this setting we analyse two transference inequalities obtained by Schmidt and Summerer. We present a rather simple geometric observation, which proves their result. We also derive several corollaries previously unknown. Particularly, we show that, together with the transference inequalities for uniform exponents, Schmidt and Summerer's inequalities imply the inequalities by Bugeaud and Laurent and "one half" of the inequalities by Marnat and Moshchevitin. Besides that, we show that our main construction provides a rather simple proof of Nesterenko's linear independence criterion.
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