论文标题
圆润的实用指南
A practical guide to well roundedness
论文作者
论文摘要
令$ g $为半imple代数组。我们开发了一种用于操纵和制造良好家庭的机械，$ \ left \ {\ Mathcal {b} _ {t} \ right \} _ {t> 0} \ subset g $是A. Gorodnik和A. Nevo在工作中定义的。这些类型的家庭的重要性在于，一个人可以渐近地计算其中的晶格点，甚至获得错误术语。晶格计数非常有效地从数字理论和数字的几何形状中解决渐近问题。 我们开发的工具很方便，尤其是在家庭获得W.R.T. $ g $（例如iwasawa或cartan）的某些分解以及当它取决于$ \ mathcal {m}/h $的子品质时，其中$ \ mathcal {m} \ subset g $是一个submanifold，submanifold和$ h <g $是封闭的子组。
Let $G$ be a semisimple algebraic group. We develop a machinery for manipulation and manufacture of well-rounded families $\left\{ \mathcal{B}_{T}\right\} _{T>0}\subset G$ as they were defined in a work by A. Gorodnik and A. Nevo. The importance of these types of families is that one can asymptotically count lattice points in them and even obtain an error term. Lattice counting is highly effective for solving asymptotic problems from number theory and the geometry of numbers. The tools we develop are handy especially when the family is given w.r.t. some decomposition of $G$ (e.g. Iwasawa or Cartan) and also when it depends upon a sub-quotients of the form $\mathcal{M}/H$, where $\mathcal{M}\subset G$ is a submanifold and $H<G$ is a closed subgroup.
