Mathematics > Number Theory
[Submitted on 12 Mar 2018]
Title:A note on $p$-adic locally analytic functions with application to behavior of the $p$-adic valuations of Stirling numbers
View PDFAbstract:The aim of this paper is to prove conjectures concerning $p$-adic valuations of Stirling numbers of the second kind $S(n,k)$, $n,k\in\mathbb{N}_+$, stated by Amdeberhan, Manna and Moll and Berrizbeitia et al., where $p$ is a prime number. The proof is based on elementary facts from $p$-adic analysis.
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