On higher order generalized Bernoulli numbers

摘要

In this paper, we define higher order generalized Bernoulli numbers in order to give the values of a series attached to Dirichlet character at non-positive integers, and investigate the arithmetic properties of them. In particular, we obtain Euler summation formula involving higher order generalized Bernoulli numbers. Also, in the p-adic cyclotomic field, we construct Witt’s type formula involving higher order generalized Bernoulli numbers.