论文标题
数字的多参数几何及其应用于分裂转移定理的应用
Multiparametric geometry of numbers and its application to splitting transference theorems
论文作者
论文摘要
在本文中，我们考虑了Wolfgang Schmidt和Leonard Summerer数字的参数几何形状的多参数版本。我们在两种设置中应用这种方法：第一种方法涉及加权二磷酸近似，第二种方法涉及晶格的二磷剂指数。在这两种情况下，我们都使用多参数方法来定义中间指数。然后，我们将dyson的转移定理的加权版本和khintchine的转移定理的类似物分配给了晶格的Diophantine指数，以分为我们在参数方法提供的直觉上定义基础的中间指数之间的不平等链中的链。
In this paper we consider a multiparametric version of Wolfgang Schmidt and Leonard Summerer's parametric geometry of numbers. We apply this approach in two settings: the first one concerns weighted Diophantine approximation, the second one concerns Diophantine exponents of lattices. In both settings we use multiparametric approach to define intermediate exponents. Then we split the weighted version of Dyson's transference theorem and an analogue of Khintchine's transference theorem for Diophantine exponents of lattices into chains of inequalities between the intermediate exponents we define basing on the intuition provided by the parametric approach.
