Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Multi-variable Rankin-Selberg Integral for a Product of $GL_2$-twisted
  Spinor $L$-functions   We consider a new integral representation for $L(s_1, \Pi \times \tau_1)
L(s_2, \Pi \times \tau_2),$ where $\Pi$ is a globally generic cuspidal
representation of $GSp_4,$ and $\tau_1$ and $\tau_2$ are two cuspidal
representations of $GL_2$ having the same central character. As and
application, we find a new period condition for two such $L$ functions to have
a pole simultaneously. This points to an intriguing connection between a
Fourier coefficient of a residual representation on $GSO(12)$ and a theta
function on $\widetilde{Sp}(16).$ A similar integral on $GSO(18)$ fails to
unfold completely, but in a way that provides further evidence of a connection.

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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph