Stirling numbers with level 2 and poly-Bernoulli numbers with level 2

2021/04/20 by Takao Komatsu, Komatsu, Takao · 1 citation
Mathematics · #05A15 #05A19 #11A07 #11B37 #11B68 #11B73 #11B75 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.09726

openalex publication_date 2021/04/20 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce poly-Bernoulli numbers with level 2, related to the Stirling numbers of the second kind with level 2, and study several properties of poly-Bernoulli numbers with level 2 from their expressions, relations, and congruences. Poly-Bernoulli numbers with level 2 have strong connections with poly-Cauchy numbers with level 2. In a special case, we can determine the denominators of Bernoulli numbers with level 2 by showing a von Staudt-Clausen like theorem.

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