一个实用的指南，以良好的全面
A practical guide to well roundedness
摘要：
设$G$是半单代数群.我们开发了一种用于操纵和制造全面的家族$\left\{ \mathcal{B}_{T}\right\} _{T>0}\subset G$的机器，因为它们在A. Gorodnik和A.尼沃这些类型的家庭的重要性是，一个可以渐近计算格点，甚至获得一个错误的条款。格计数对于解决数论和数的几何中的渐近问题是非常有效的。我们开发的工具很方便，特别是当家庭被赋予w.r.t. $G$的某些分解（例如Iwasawa或Cartan），以及当它依赖于$\mathcal{M}/H$形式的子流形时，其中$\mathcal{M}\subset G$是子流形，$H<G$是闭子群。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
