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A local-global theorem for $p$-adic supercongruences | | Hao Pan
; Roberto Tauraso
; Chen Wang
; | | Date: |
18 Sep 2019 | | Abstract: | 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. | | Source: | arXiv, 1909.8183 | | Services: | Forum | Review | PDF | Favorites | |
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