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

2018/03/12 by Piotr Miska, Miska, Piotr
Mathematics · #11B73 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1803.04533

openalex publication_date 2018/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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∈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.

Related

• New results on the p-adic valuation of Stirling numbers
• The 2-adic valuations of Stirling numbers
• On the p-adic properties of Stirling numbers of the first kind
• The 2-adic valuations of differences of Stirling numbers of the second kind
• Congruence classes of 2-adic valuations of Stirling numbers of the second kind