Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Theta Correspondence, Periods of Automorphic Forms and Special
  Values of Standard Automorphic L-Functions   The zeros and poles of standard automorphic $L$-functions attached to
representations of classical groups are linked to the nonvanishing of lifts in
the theory of the theta correspondence. The results of this paper show that
when a cuspidal representation $\sigma$ of a symplectic group $G$ lifts to a
cuspidal representation $\pi = \theta_{\psi}(\sigma)$ of an orthogonal group
$H$ attached to a quadratic space $V$ of dimension $m$, the Fourier
coefficients of automorphic forms in $\sigma$ are linked to periods of
automorphic forms in $\pi$. Consequently, when our results are combined with
the Rallis inner product formula in the convergent range or the second term
range, we prove a special value formula for the standard automorphic
$L$-function $L(s,\sigma,\chi_V)$ attached to $\sigma$ (and twisted by the
character $\chi_V$ of $V$) at the point $s_{m,2n}=m/2-(2n+1)/2$ in terms of the
Fourier coefficients of automorphic forms in $\sigma$ and periods of forms in
$\pi$.

22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex