Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Product of Tensor Product $L$-functions of Quasi-split Classical
  Groups of Hermitian Type   A family of global integrals representing a product of tensor product
(partial) $L$-functions: $ L^S(s,\pi\times\tau_1)L^S(s,\pi\times\tau_2)...
L^S(s,\pi\times\tau_r) $ are established in this paper, where $\pi$ is an
irreducible cuspidal automorphic representation of a quasi-split classical
group of Hermitian type and $\tau_1,...,\tau_r$ are irreducible unitary
cuspidal automorphic representations of $\GL_{a_1},...,\GL_{a_r}$,
respectively. When $r=1$ and the classical group is an orthogonal group, this
was studied by Ginzburg, Piatetski-Shapiro and Rallis in 1997 and when $\pi$ is
generic and $\tau_1,...,\tau_r$ are not isomorphic to each other, this is
considered by Ginzburg, Rallis and Soudry in 2011. In this paper, we prove that
the global integrals are eulerian and finish the explicit calculation of
unramified local $L$-factors in general. The remaining local and global theory
for this family of global integrals will be considered in our future work.

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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph