Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Klein quartic maximizes the multiplicity of the first positive
  eigenvalue of the Laplacian   We prove that Klein quartic maximizes the multiplicity of the first positive
eigenvalue of the Laplacian among all closed hyperbolic surfaces of genus $3$,
with multiplicity equal to $8$. We also obtain partial results in genus $2$,
where we find that the maximum multiplicity is between $3$ and $6$. Along the
way, we show that for every $g\geq 2$, there exists some $\delta_g>0$ such that
the multiplicity of any eigenvalue of the Laplacian on a closed hyperbolic
surface of genus $g$ in the interval $[0,1/4+\delta_g]$ is at most $2g-1$
despite the fact that this interval can contain arbitrarily many eigenvalues.
This extends a result of Otal to a larger interval but with a weaker bound,
which nevertheless improves upon the general upper bound of S\'evennec.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph