Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On integrals of eigenfunctions over geodesics   If $(M,g)$ is a compact Riemannian surface then the integrals of
$L^2(M)$-normalized eigenfunctions $e_j$ over geodesic segments of fixed length
are uniformly bounded. Also, if $(M,g)$ has negative curvature and $\gamma(t)$
is a geodesic parameterized by arc length, the measures $e_j(\gamma(t))\, dt$
on $\R$ tend to zero in the sense of distributions as the eigenvalue $\la_j\to
\infty$, and so integrals of eigenfunctions over periodic geodesics tend to
zero as $\la_j\to \infty$. The assumption of negative curvature is necessary
for the latter result.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph