论文标题
扭曲表示的合理性
Rationality of twist representation zeta functions of compact $p$-adic analytic groups
论文作者
论文摘要
我们证明，对于任何扭曲的紧凑型$ p $ -Adic分析组$ g $，其扭曲表示Zeta Zeta函数是$ n_ {i}^{ - s} f_ {i} f_ {i}（p^{ - s}）$的有限总和功能。 Zeta功能的横坐标的Meromorthic延续和合理性随着推论。如果$ g $也是Pro-P $组，我们证明其扭曲表示Zeta函数在$ p^{ - s} $中是合理的。为了建立这些结果，我们开发了一种克利福德理论，用于扭曲的同类体，包括扭曲等值镜的新的共同体理论不变。 Arxiv的第二部分：2007.10694。
We prove that for any twist rigid compact $p$-adic analytic group $G$, its twist representation zeta function is a finite sum of terms $n_{i}^{-s}f_{i}(p^{-s})$, where $n_{i}$ are natural numbers and $f_{i}(t)\in\mathbb{Q}(t)$ are rational functions. Meromorphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If $G$ is moreover a pro-$p$ group, we prove that its twist representation zeta function is rational in $p^{-s}$. To establish these results we develop a Clifford theory for twist isoclasses of representations, including a new cohomological invariant of a twist isoclass. Second part of arXiv:2007.10694.
