Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectrum of weighted adjacency operator on a non-uniform arithmetic
  quotient of $PGL_3$   We investigate the automorphic spectra of the natural weighted adjacency
operator on the complex arising as a $PGL(3,\mathbb{F}_q[t])$ quotient of
$\widetilde{A}_2$-type building. We prove that the set of non-trivial
approximate eigenvalues $(\lambda^+,\lambda^-)$ of the weighted adjacency
operators $A_w^\pm$ on the quotient induced from the colored adjacency
operators $A^\pm$ on the building for $PGL_3$ contains the simultaneous
spectrum of $A^\pm$ and another hypocycloid with three cusps. As a byproduct,
we re-establish a proof of the fact that $PGL(3,\mathbb{F}_q[t])\backslash
PGL(3,\mathbb{F}_q(\!(t^{-1})\!))/PGL(3,\mathbb{F}_q[\![t^{-1}]\!])$ is not a
Ramanujan complex, from a combinatorial aspect.

31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org