Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining Optimal Test Functions for Bounding the Average Rank in
  Families of $L$-Functions   Given an $L$-function, one of the most important questions concerns its
vanishing at the central point; for example, the Birch and Swinnerton-Dyer
conjecture states that the order of vanishing there of an elliptic curve
$L$-function equals the rank of the Mordell-Weil group. The Katz and Sarnak
Density Conjecture states that this and other behavior is well-modeled by
random matrix ensembles. This correspondence is known for many families when
the test functions are suitably restricted. For appropriate choices, we obtain
bounds on the average order of vanishing at the central point in families. In
this note we report on progress in determining the optimal test functions for
the various classical compact groups for different support restrictions, and
discuss how this relates to improved rank bounds.

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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat