Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second Moment of the Prime Geodesic Theorem for $\mathrm{PSL}(2,
  \mathbb{Z}[i])$   The remainder $E_\Gamma(X)$ in the Prime Geodesic Theorem for the Picard
group $\Gamma = \mathrm{PSL}(2,\mathbb{Z}[i])$ is known to be bounded by
$O(X^{3/2+\epsilon})$ under the assumption of the Lindel\"of hypothesis for
quadratic Dirichlet $L$-functions over Gaussian integers. By studying the
second moment of $E_\Gamma(X)$, we show that on average the same bound holds
unconditionally.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: funct-an