Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pair correlation densities of inhomogeneous quadratic forms   Under explicit diophantine conditions on $(\alpha,\beta)\in\RR^2$, we prove
that the local two-point correlations of the sequence given by the values
$(m-\alpha)^2+\break (n-\beta)^2$, with $(m,n)\in\ZZ^2$, are those of a Poisson
process. This partly confirms a conjecture of Berry and Tabor [2] on spectral
statistics of quantized integrable systems, and also establishes a particular
case of the quantitative version of the Oppenheim conjecture for inhomogeneous
quadratic forms of signature (2,2). The proof uses theta sums and Ratner's
classification of measures invariant under unipotent flows.

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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ