Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The fourth moment of quadratic Dirichlet $L$-functions   We study the fourth moment of quadratic Dirichlet $L$-functions at $s=
\frac{1}{2}$. We show an asymptotic formula under the generalized Riemann
hypothesis, and obtain a precise lower bound unconditionally. The proofs of
these results follow closely arguments of Soundararajan and Young [19] and
Soundararajan [17].

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio