Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A smooth shift approach for a Ramanujan expansion   All arithmetical functions $F$ satisfying Ramanujan Conjecture, i.e.,
$F(n)\ll_{\varepsilon}n^{\varepsilon}$, and with $Q-$smooth divisors, i.e.,
with Eratosthenes transform $F':=F\ast \mu$ supported in $Q-$smooth numbers,
have a kind of unique Ramanujan expansion; also, these Ramanujan coefficients
decay very well to $0$ and have two explicit expressions (in the style of
Carmichael and Wintner). This general result, then, is applied to the
shift-Ramanujan expansions, i.e., the expansions for correlations with respect
to the shift, whence the title.

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The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
16
The categories of this paper are: stat
3
The categories of this paper are: physics