Congruences among generalized Bernoulli numbers

Janusz Szmidt; Jerzy Urbanowicz; Don Zagier

Acta Arithmetica (1995)

  • Volume: 71, Issue: 3, page 273-278
  • ISSN: 0065-1036

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Janusz Szmidt, Jerzy Urbanowicz, and Don Zagier. "Congruences among generalized Bernoulli numbers." Acta Arithmetica 71.3 (1995): 273-278. <http://eudml.org/doc/206775>.

@article{JanuszSzmidt1995,
author = {Janusz Szmidt, Jerzy Urbanowicz, Don Zagier},
journal = {Acta Arithmetica},
keywords = {Dirichlet’s -function; generalized Bernoulli numbers; Bernoulli polynomials; divisibility; class numbers; quadratic fields},
language = {eng},
number = {3},
pages = {273-278},
title = {Congruences among generalized Bernoulli numbers},
url = {http://eudml.org/doc/206775},
volume = {71},
year = {1995},
}

TY - JOUR
AU - Janusz Szmidt
AU - Jerzy Urbanowicz
AU - Don Zagier
TI - Congruences among generalized Bernoulli numbers
JO - Acta Arithmetica
PY - 1995
VL - 71
IS - 3
SP - 273
EP - 278
LA - eng
KW - Dirichlet’s -function; generalized Bernoulli numbers; Bernoulli polynomials; divisibility; class numbers; quadratic fields
UR - http://eudml.org/doc/206775
ER -

References

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  1. [1] B. C. Berndt, Character analogues of the Poisson and Euler-Maclaurin summation formula with applications, J. Number Theory 7 (1975), 413-445. Zbl0316.10023
  2. [2] B. C. Berndt, Classical theorems on quadratic residues, Enseign. Math. 22 (1976), 261-304. Zbl0337.10031
  3. [3] L. Carlitz, Arithmetic properties of generalized Bernoulli numbers, J. Reine Angew. Math. 202 (1959), 174-182. Zbl0125.02202
  4. [4] G. Gras, Relations congruentielles linéaires entre nombres de classes de corps quadratiques, Acta Arith. 52 (1989), 147-162. Zbl0618.12004
  5. [5] K. Hardy and K. S. Williams, A congruence relating to class numbers of complex quadratic fields, Acta Arith. 47 (1986), 263-276. Zbl0557.12003
  6. [6] H. W. Leopoldt, Eine Verallgemeinerung der Bernoullischen Zahlen, Abh. Math. Sem. Univ. Hamburg 22 (1958), 131-140. Zbl0080.03002
  7. [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. [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. [9] T. Uehara, On linear congruences between class numbers of quadratic fields, J. Number Theory 34 (1990), 362-392. Zbl0693.12006
  10. [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. Zbl0706.11058
  11. [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. Zbl0706.11059
  12. [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. 

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