Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth Sums over Smooth $k$-Free Numbers and Statistical Mechanics   We provide an asymptotic estimate for certain sums over k-free integers with
small prime factors. These sums depend upon a complex parameter \alpha and
involve a smooth cut-off f. They are a variation of several classical
number-theoretical sums. One term in the asymptotics is an integral operator
whose kernel is the \alpha-convolution of the Dickman-de Bruijn distribution,
and the other term is explicitly estimated. The trade-off between the value of
\alpha and the regularity of f is discussed. This work generalizes the results
of tow previous papers by the author and Ya.G. Sinai, where k=2 and \alpha=1.

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The categories of this paper are: patt-sol
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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: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th