Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maass waveforms and low-lying zeros   The Katz-Sarnak Density Conjecture states that the behavior of zeros of a
family of $L$-functions near the central point (as the conductors tend to zero)
agrees with the behavior of eigenvalues near 1 of a classical compact group (as
the matrix size tends to infinity). Using the Petersson formula, Iwaniec, Luo
and Sarnak proved that the behavior of zeros near the central point of
holomorphic cusp forms agrees with the behavior of eigenvalues of orthogonal
matrices for suitably restricted test functions $\phi$. We prove similar
results for families of cuspidal Maass forms, the other natural family of ${\rm
GL}_2/\mathbb{Q}$ $L$-functions. For suitable weight functions on the space of
Maass forms, the limiting behavior agrees with the expected orthogonal group.
We prove this for $\Supp(\widehat{\phi})\subseteq (-3/2, 3/2)$ when the level
$N$ tends to infinity through the square-free numbers; if the level is fixed
the support decreases to being contained in $(-1,1)$, though we still uniquely
specify the symmetry type by computing the 2-level density.

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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas