Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: G\'al-type GCD sums beyond the critical line   We prove that \[ \sum_{k,{\ell}=1}^N\frac{(n_k,n_{\ell})^{2\alpha}}{(n_k
n_{\ell})^{\alpha}} \ll N^{2-2\alpha} (\log N)^{b(\alpha)} \] holds for
arbitrary integers $1\le n_1<\cdots < n_N$ and $0<\alpha<1/2$ and show by an
example that this bound is optimal, up to the precise value of the exponent
$b(\alpha)$. This estimate complements recent results for $1/2\le \alpha \le 1$
and shows that there is no "trace" of the functional equation for the Riemann
zeta function in estimates for such GCD sums when $0<\alpha<1/2$.

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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs