Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Autocorrelation of the Mobius Function   This article provides an asymptotic result for the autocorrelation function
$\sum_{n \leq x} \mu(n) \mu(n+a) =O \left (x\log^{-c}x \right )$ of the Mobius
function $\mu$, based on standard analytic methods, where $a\ne0$ is a fixed
parameter, and $c>0$ is a constant.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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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: eess
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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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: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc