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ArticleOriginal scientific text

Title

Congruences among generalized Bernoulli numbers

Authors 1, 2, 3

Affiliations

  1. Institute of Mathematics, Military Academy of Technology, ul. Kaliskiego 2, 01-489 Warszawa, Poland
  2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
  3. Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, D-53225 Bonn, Germany

Bibliography

  1. B. C. Berndt, Character analogues of the Poisson and Euler-Maclaurin summation formula with applications, J. Number Theory 7 (1975), 413-445.
  2. B. C. Berndt, Classical theorems on quadratic residues, Enseign. Math. 22 (1976), 261-304.
  3. L. Carlitz, Arithmetic properties of generalized Bernoulli numbers, J. Reine Angew. Math. 202 (1959), 174-182.
  4. G. Gras, Relations congruentielles linéaires entre nombres de classes de corps quadratiques, Acta Arith. 52 (1989), 147-162.
  5. K. Hardy and K. S. Williams, A congruence relating to class numbers of complex quadratic fields, Acta Arith. 47 (1986), 263-276.
  6. H. W. Leopoldt, Eine Verallgemeinerung der Bernoullischen Zahlen, Abh. Math. Sem. Univ. Hamburg 22 (1958), 131-140.
  7. M. Lerch, Essai sur le calcul du nombre de classes de formes quadratiques binaires aux coefficients entiers, Acta Math. 29 (1905), 333-424.
  8. J. Szmidt and J. Urbanowicz, Some new congruences for generalized Bernoulli numbers of higher orders, preprint FI94-LF05 of the Fields Institute for Research in Math. Sciences.
  9. T. Uehara, On linear congruences between class numbers of quadratic fields, J. Number Theory 34 (1990), 362-392.
  10. J. Urbanowicz, Connections between B₂,χ for even quadratic Dirichlet characters χ and class numbers of appropriate imaginary quadratic fields I, Compositio Math. 75 (1990), 247-270, Corrigendum: Compositio Math. 77 (1991), 119-123.
  11. J. Urbanowicz, Connections between B₂,χ for even quadratic Dirichlet characters χ and class numbers of appropriate imaginary quadratic fields II, Compositio Math. 75 (1990), 271-285, Corrigendum: Compositio Math. 77 (1991), 123-125.
  12. J. Urbanowicz, On some new congruences for generalized Bernoulli numbers, I and II, Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, Années 1990/91.
Acta Arithmetica
1995/71/3
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Pages:
273-278
Main language of publication
English
Received
1994-08-28
Accepted
1995-02-10
Published
1995
Exact and natural sciences