Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A local-global theorem for $p$-adic supercongruences   Let ${\mathbb Z}_p$ denote the ring of all $p$-adic integers and call
$${\mathcal U}=\{(x_1,\ldots,x_n):\,a_1x_1+\ldots+a_nx_n+b=0\}$$ a hyperplane
over ${\mathbb Z}_p^n$, where at least one of $a_1,\ldots,a_n$ is not divisible
by $p$. We prove that if a sufficiently regular $n$-variable function is zero
modulo $p^r$ over some suitable collection of $r$ hyperplanes, then it is zero
modulo $p^r$ over the whole ${\mathbb Z}_p^n$. We provide various applications
of this general criterion by establishing several $p$-adic analogues of
hypergeometric identities.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th