Congruence properties of generalized Bernoulli numbers play an important role in many fields of number theory. Here denotes a character with the conductor , and the numbers are defined by
Let be a prime, be a character with conductor and , a character which differs from only by the Legendre symbol modulo then the following congruences (Theorem 1) hold: , where and .
Continuing his studies the author proves some von Staudt’s type congruences of the form if and , see Theorem 2. Finally he applies his results to quadratic number fields, showing that these congruences are -adic approximations of the class number formula.