On the generalized Bernoulli numbers that belong to unequal characters

• Autores: Ilya Sh. Slavutskii
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 16, Nº 3, 2000, págs. 459-475
• Idioma: inglés
• DOI: 10.4171/rmi/280
• Títulos paralelos:
  • Sobre los números de Bernoulli generalizados que pertenecen a caracteres desiguales
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• Resumen

  • 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.