Generalized Bernoulli numbers and congruence of modular forms (Q1115470)

Using the theory developed by Hida, the author gives a sufficient condition for the existence of families of congruent ordinary modular forms. The criterion is one of p-divisibility of a certain generalized Bernoulli number. Under the same condition the author proves that (in certain cases) certain special values (the Hurwitz-Damerell numbers) of Hecke L-functions are also divisible by p.