论文标题
$ p $ - 亚种模型理论，$ p $ - 亚种积分，欧拉产品和zeta函数组的Zeta功能
$p$-adic model theory, $p$-adic integrals, Euler products, and zeta functions of groups
论文作者
论文摘要
我们对DENEF的理性定理进行了调查，该定理在$ p $ - adic积分，$ p $版本中的统一，相关模型理论以及对有限生成的nilpotent群体和共轭类的亚组进行了许多应用程序，以及雪佛兰集团全部集团本地领域的一致性群体中的一致性。然后，我们在所有$ p $上陈述了此类$ p $ - adic积分的Euler产品的分析性能，并在某些代数组的一致性中计数一致性的商品对合理群的一致性计数。然后，我们简要讨论Zeta功能是由可定义的等效关系和$ p $ -ADIC消除Imginaries引起的，这些功能在计数群体的表示方面有应用。
We give a survey of Denef's rationality theorem on $p$-adic integrals, its uniform in $p$ versions, the relevant model theory, and a number of applications to counting subgroups of finitely generated nilpotent groups and conjugacy classes in congruence quotients of Chevalley groups over rings of integers of local fields. We then state results on analytic properties of Euler products of such $p$-adic integrals over all $p$, and an application to counting conjugacy classes in congruence quotients of certain algebraic groups over the rationals. We then briefly discuss zeta functions arising from definable equivalence relations and $p$-adic elimination of imginaries, which have applications to counting representations of groups.
