Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rationality of representation zeta functions of compact $p$-adic
  analytic groups   We prove that for any FAb compact $p$-adic analytic group $G$, its
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 representation zeta function is
rational in $p^{-s}$. These results were proved by Jaikin-Zapirain for $p>2$ or
for $G$ uniform and pro-$2$, respectively. We give a new proof which avoids the
Kirillov orbit method and works for all $p$. Moreover, we prove analogous
results for twist zeta functions of compact $p$-adic analytic groups, which
enumerate irreducible representations up to one-dimensional twists. In the
course of the proof, we develop a Clifford theory for twist isoclasses of
representations, including a new cohomological invariant of a twist isoclass.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph