Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Test vectors for local cuspidal Rankin-Selberg integrals of GL(n), and
  reduction modulo $\ell$   Let $\pi_1,\pi_2$ be a pair of cuspidal complex, or $\ell$-adic,
representations of the general linear group of rank $n$ over a non-archimedean
local field $F$ of residual characteristic $p$, different to $\ell$. Whenever
the local Rankin-Selberg $L$-factor $L(X,\pi_1,\pi_2)$ is nontrivial, we
exhibit explicit test vectors in the Whittaker models of $\pi_1$ and $\pi_2$
such that the local Rankin-Selberg integral associated to these vectors and to
the characteristic function of $\mathfrak{o}_F^n$ is equal to
$L(X,\pi_1,\pi_2)$. We give an initial application of the test vectors to
reduction modulo $\ell$ of $\ell$-adic $L$-factors.

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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th