A note on $p$-adic locally analytic functions with application to behavior of the $p$-adic valuations of Stirling numbers

Abstract

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.

To appear in Acta Arithmetica

References in corpus (1)

• Congruence classes of 2-adic valuations of Stirling numbers of the second kind