Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier Coefficients of Automorphic Forms and Integrable Discrete Series   Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group
$\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and
noncompact. We study Fourier coefficients of Poincar\' e series attached to
matrix coefficients of integrable discrete series. We use these results to
construct explicit automorphic cuspidal realizations, which have appropriate
Fourier coefficients $\neq 0$, of integrable discrete series in families of
congruence subgroups. In the case of $G=Sp_{2n}(\mathbb R)$, we relate our work
to that of Li [15]. For $\mathcal G$ quasi--split over $\mathbb Q$, we relate
our work to the result about Poincar\' e series due to Khare, Larsen, and Savin
[16].

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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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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: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex