Congruences among generalized Bernoulli numbers

• Autorzy: Janusz Szmidt , Jerzy Urbanowicz , Don Zagier
• Języki publikacji: EN

Kategorie tematyczne

• 11R42: Zeta functions and L -functions of number fields
• 11M06: ζ ( s ) and L ( s , χ )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 71
• Numer: 3
• Strony: 273-278

Daty

wydano

1995

otrzymano

1994-08-28

poprawiono

1995-02-10

Twórcy

autor

Janusz Szmidt

• Institute of Mathematics, Military Academy of Technology, ul. Kaliskiego 2, 01-489 Warszawa, Poland

autor

Jerzy Urbanowicz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

autor

Don Zagier

• Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, D-53225 Bonn, Germany

Bibliografia

• [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.