A congruence concerning a convolution involving weighted Bernoulli numbers

2021/11/03 by Claire I. Levaillant, Levaillant, Claire I.
Mathematics · #05A05 #11B68 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A05 #msc:11B68

paper · pdf · doi:10.48550/arxiv.2111.02103

12 pages, 22 references

arxiv created 2021/11/05 · arxiv updated 2021/11/08

Abstract

Given a prime p≥ 5, we reduce modulo p a convolution of order p-1 of powers of two weighted Bernoulli numbers with Bernoulli numbers in terms of harmonic numbers and generalized harmonic numbers. Our proof is based on studying the p-adic expansion of the number of permutations of Sym(p-2) with an even number of ascents, up to the modulus p².

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