Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: GCD sums and complete sets of square-free numbers   It is proved that \[ \sum_{k,{\ell}=1}^N\frac{\gcd(n_k,n_{\ell})}{\sqrt{n_k
n_{\ell}}} \ll N\exp\left(C\sqrt{\frac{\log N \log\log\log N}{\log\log
N}}\right) \] holds for arbitrary integers $1\le n_1<\cdots < n_N$. This bound
is essentially better than that found in a recent paper of Aistleitner, Berkes,
and Seip and can not be improved by more than possibly a power of
$1/\sqrt{\log\log\log N}$. The proof relies on ideas from classical work of
G\'{a}l, the method of Aistleitner, Berkes, and Seip, and a certain
completeness property of extremal sets of square-free numbers.

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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess