Some congruences involving generalized Bernoulli numbers and Bernoulli polynomials

2022/11/29 by Ni Li, Li, Ni, Ma Rong +1 · 1 citation
Mathematics · #11A07 #11B68 #Advanced Mathematical Identities #Analytic Number Theory Research #B.2 #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2211.15874

openalex publication_date 2022/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let [x] be the integral part of x, n>1 be a positive integer and χ_n denote the trivial Dirichlet character modulo n. In this paper, we use an identity established by Z. H. Sun to get congruences of T_m,k(n)=∑_x=1^[n/m](χ_n(x))/(x^k)(\bmod n^r+1) for r∈ \1,2\, any positive integer m with n ≡ ± 1 (\bmod m ) in terms of Bernoulli polynomials. As its an application, we also obtain some new congruences involving binomial coefficients modulo n⁴ in terms of generalized Bernoulli numbers.

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