Bernoulli numbers in p-adic analysis

摘要

In this paper we consider new representations of the analogue higher order Bernoulli numbers in p-adic analysis. Also, we prove Kummer-type congruence for these numbers using Ota’s method [J. Number Theory 92 (2002) 1], which is a solution to a part of the Question 2 in the paper by Jang and Kim [Appl. Math. Comput. 137 (2,3) (2003) 387].