Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sums of weighted averages of gcd-sum functions II   In this paper, we establish the following two identities involving the Gamma
function and Bernoulli polynomials, namely $$ \sum_{k\leq x}\frac{1}{k^s}
\sum_{j=1}^{k^s}\log\Gamma\left(\frac{j}{k^s}\right)
  \sum_{\substack{d|k \\ d^{s}|j}}f*\mu(d) \quad {\rm and } \quad \sum_{k\leq
x}\frac{1}{k^s}\sum_{j=0}^{k^{s}-1}
  B_{m}\sum_{\substack{d|k \\ d^{s}|j}} f*\mu(d) $$ with any fixed integer $s>
1$ and any arithmetical function $f$. We give asymptotic formulas for them with
various multiplicative functions $f$. We also consider several formulas of the
Dirichlet series associated with the above identities. This paper is a
continuation of an earlier work of the authors.

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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: funct-an