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

Piotr Miska

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

Number Theory 2018-03-14 v1

Authors: Piotr Miska

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.

Keywords

p-adic locally analytic functions p-adic valuations stirling numbers of the second kind prime numbers p-adic analysis

Cite

@article{arxiv.1803.04533,
  title  = {A note on $p$-adic locally analytic functions with application to behavior of the $p$-adic valuations of Stirling numbers},
  author = {Piotr Miska},
  journal= {arXiv preprint arXiv:1803.04533},
  year   = {2018}
}

Comments

To appear in Acta Arithmetica

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