Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric approach to the sup-norm problem for automorphic forms: the
  case of newforms on $GL_2(\mathbb F_q(T))$ with squarefree level   The sup-norm problem in analytic number theory asks for the largest value
taken by a given automorphic form. We observe that the function-field version
of this problem can be reduced to the geometric problem of finding the largest
dimension of the $i$th stalk cohomology group of a given Hecke eigensheaf at
any point. This problem, in turn, can be reduced to the intersection-theoretic
problem of bounding the "polar multiplicities" of the characteristic cycle of
the Hecke eigensheaf, which in known cases is the nilpotent cone of the moduli
space of Higgs bundles. We solve this problem for newforms on $GL_2 (\mathbb
A_{\mathbb F_q(t)})$ of squarefree level, leading to bounds on the sup-norm
that are stronger than what is known in the analogous problem for newforms on
$GL_2(\mathbb A_{\mathbb Q})$ (i.e. classical holomorphic and Maass modular
forms.)

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex