Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The split case of the Prasad--Takloo-Bighash conjecture for cuspidal
  representations of level zero   Let $E/F$ be a quadratic extension of non archimedean local fields of odd
residual characteristic. We prove a conjecture of Prasad and Takloo-Bighash, in
the case of cuspidal representations of depth zero of $\mathrm{GL}(2m,F)$. This
conjecture characterizes distinction for the pair
$(\mathrm{GL}(2m,F),\mathrm{GL}(m,E))$ with respect to a character $\mu\circ
\mathrm{det}$ of $\mathrm{GL}(m,E)$, in terms of certain conditions on
Langlands paremeters, including an epsilon value. We also compute the
multiplicity of the involved equivariant linear forms when $E/F$ is unramified,
and also when $\mu$ is tame. In both cases this multiplicity is at most one.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn