Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates from below for the spectral function and for the remainder in
  local Weyl's law   We obtain asymptotic lower bounds for the spectral function of the Laplacian
and for the remainder in local Weyl's law on manifolds. In the negatively
curved case, thermodynamic formalism is applied to improve the estimates. Key
ingredients of the proof include the wave equation parametrix, a pretrace
formula and the Dirichlet box principle. Our results develop and extend the
unpublished thesis of A. Karnaukh.

8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys