Resumen de On the generalized Bernoulli numbers that belong to unequal characters
Ilya Sh. Slavutskii
The study of class number invariants of absolute abelian fields, the investigation of congruences for special values of L-functions, Fourier coefficients of half-integral weight modular forms, Rubin's congruences involving the special values of L-functions of elliptic curves with complex multiplication, and many other problems require congruence properties of the generalized Bernoulli numbers (see [16]-[18], [12], [29], [3], etc.). The first steps in this direction can be found in the papers of H. W. Leopoldt (see [15]) and L. Carlitz (see [5]). For further studies, see [22], [24], [29]. This paper presents some new examples extending both old author's results and recent investigations of H. Lang (see [14]), A. Balog , H. Darmon, K. Ono (see [3]), etc. On the whole the proved results are consequence of congruences connecting the generalized Bernoulli numbers that belong to unequal characters.
