论文标题
经典类型的Bruhat-tits建筑物中的简单卷
Simplicial volumes in Bruhat-Tits buildings of split classical type
论文作者
论文摘要
在拆分经典类型的bruhat-tits建筑中（即$ a_n $，$ b_n $，$ c_n $，$ d_n $以及它们的任何组合）中，在本地字段中，简单卷计为给定的简单距离内的顶点。本文旨在研究简单量的渐近生长。简单体积的公式是从凹函数理论中得出的。然后，使用本文开发的$ q $ - 指数多项式的理论发现了其渐近生长中的主要术语。
In a Bruhat-Tits building of split classical type (that is, of type $A_n$, $B_n$, $C_n$, $D_n$, and any combination of them) over a local field, the simplicial volume counts the vertices within the given simplicial distance from a special vertex. This paper aims to study the asymptotic growth of the simplicial volume. A formula of the simplicial volume is deduced from the theory of concave functions. Then the dominant term in its asymptotic growth is found using the theory of $q$-exponential polynomials developed in this paper.
