论文标题
使用本地Zeta积分计算表代数订单的Zeta函数
Computing zeta functions of table algebra orders using local zeta integrals
论文作者
论文摘要
我们研究所罗门的ZETA功能，该命令是由积分表代数的标准基础生成的订单的特殊情况，一种特殊情况是关联方案的积分邻接代数。由于所罗门用于计算此ZETA函数的基本方法会陷入$ 3 $或更多等级的计算困难，因此需要更有效的方法。我们提供了几个示例，以说明如何将Bushnell和Reiner提出的局部Zeta积分方法应用于计算这些顺序的显式Zeta函数。
We investigate Solomon's zeta function for orders in the special case of orders generated by the standard basis of an integral table algebra, a special case of which is the integral adjacency algebra of an association scheme. As Solomon's elementary method for computing this zeta function runs into computational difficulties for ranks $3$ or more, a more efficient method is desired. We give several examples to illustrate how the local zeta integral approach proposed by Bushnell and Reiner can be applied to compute explicit zeta functions for these orders.
