Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hardy-Littlewood-Chowla conjecture on average   There has been recent interest in a hybrid form of the celebrated conjectures
of Hardy-Littlewood and of Chowla. We prove that for any $k,\ell\ge1$ and
distinct integers $h_2,\ldots,h_k,a_1,\ldots,a_\ell$, we have $$\sum_{n\leq
X}\mu(n+h_1)\cdots \mu(n+h_k)\Lambda(n+a_1)\cdots\Lambda(n+a_{\ell})=o(X)$$ for
all except $o(H)$ values of $h_1\leq H$, so long as $H\geq (\log
X)^{\ell+\varepsilon}$. This improves on the range $H\ge (\log X)^{\psi(X)}$,
$\psi(X)\to\infty$, obtained in previous work of the first author. Our results
also generalize from the M\"obius function $\mu$ to arbitrary (non-pretentious)
multiplicative functions.

14
The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph