Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New test vector for Waldspurger's period integral, relative trace
  formula, and hybrid subconvexity bounds   In this paper we give quantitative local test vectors for Waldspurger's
period integral (i.e., a toric period on $\text{GL}_2$) in new cases with joint
ramifications. The construction involves minimal vectors, rather than newforms
and their variants. This paper gives a uniform treatment for the matrix algebra
and division algebra cases under mild assumptions, and establishes an explicit
relation between the size of the local integral and the finite conductor
$C(\pi\times\pi_{\chi^{-1}})$. As an application, we combine the test vector
results with the relative trace formula, and prove a hybrid type subconvexity
bound which can be as strong as the Weyl bound in proper range.

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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph