Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Traces of high powers of the Frobenius class in the hyperelliptic
  ensemble   The zeta function of a curve over a finite field may be expressed in terms of
the characteristic polynomial of a unitary symplectic matrix, called the
Frobenius class of the curve. We compute the expected value of the trace of the
n-th power of the Frobenius class for an ensemble of hyperelliptic curves of
genus g over a fixed finite field in the limit of large genus, and compare the
results to the corresponding averages over the unitary symplectic group
USp(2g). We are able to compute the averages for powers n almost up to 4g,
finding agreement with the Random Matrix results except for small n and for
n=2g. As an application we compute the one-level density of zeros of the zeta
function of the curves, including lower-order terms, for test functions whose
Fourier transform is supported in (-2,2). The results confirm in part a
conjecture of Katz and Sarnak, that to leading order the low-lying zeros for
this ensemble have symplectic statistics.

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The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th