# Connections between ${B}_{2,\chi}$ for even quadratic Dirichlet characters $\chi $ and class numbers of appropriate imaginary quadratic fields, I

Compositio Mathematica (1990)

- Volume: 75, Issue: 3, page 247-270
- ISSN: 0010-437X

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top## How to cite

topUrbanowicz, Jerzy. "Connections between $B_{2,\chi }$ for even quadratic Dirichlet characters $\chi $ and class numbers of appropriate imaginary quadratic fields, I." Compositio Mathematica 75.3 (1990): 247-270. <http://eudml.org/doc/90037>.

@article{Urbanowicz1990,

author = {Urbanowicz, Jerzy},

journal = {Compositio Mathematica},

keywords = {Birch-Tate conjecture; congruences; Milnor functor ; second generalized Bernoulli numbers; quadratic Dirichlet characters; class numbers; imaginary quadratic fields},

language = {eng},

number = {3},

pages = {247-270},

publisher = {Kluwer Academic Publishers},

title = {Connections between $B_\{2,\chi \}$ for even quadratic Dirichlet characters $\chi $ and class numbers of appropriate imaginary quadratic fields, I},

url = {http://eudml.org/doc/90037},

volume = {75},

year = {1990},

}

TY - JOUR

AU - Urbanowicz, Jerzy

TI - Connections between $B_{2,\chi }$ for even quadratic Dirichlet characters $\chi $ and class numbers of appropriate imaginary quadratic fields, I

JO - Compositio Mathematica

PY - 1990

PB - Kluwer Academic Publishers

VL - 75

IS - 3

SP - 247

EP - 270

LA - eng

KW - Birch-Tate conjecture; congruences; Milnor functor ; second generalized Bernoulli numbers; quadratic Dirichlet characters; class numbers; imaginary quadratic fields

UR - http://eudml.org/doc/90037

ER -

## References

top- [1] G. Gras: Pseudo-mesures p-adiques associees aux fonctions L de Q, Manuscripta Math.57 (1987), 373-415. Zbl0599.12016MR878131
- [2] K. Kramer and A. Candiotti: On the 2-Sylow subgroup of the Hilbert kernel of K2 of number fields, Acta Arithm.52 (1989), 49-65. Zbl0705.19005MR1005155
- [3] M. Lerch: Essai sur le calcul du nombre des classes de formes quadratiques binaires aux coefficients entiers, Acta Math.29 (1905), 333-424. JFM36.0288.12
- [4] B. Mazur and A. Wiles: Class fields of abelian extensions of Q, Invent. Math.76 (1984), 179-330. Zbl0545.12005MR742853
- [5] J. Urbanowicz: On the 2-primary part of a conjecture of Birch-Tate, Acta Arithm.43 (1983), 69-81. Zbl0529.12008MR730849
- [6] L.C. Washington: Introduction to cyclotomic fields, Springer Verlag, New York-Heidelberg -Berlin1982. Zbl0484.12001MR718674

## Citations in EuDML Documents

top- Jerzy Urbanowicz, On diophantine equations involving sums of powers with quadratic characters as coefficients, I
- Jerzy Urbanowicz, Connections between ${B}_{2,\chi}$ for even quadratic Dirichlet characters $\chi $ and class numbers of appropriate imaginary quadratic fields, II
- Jerzy Urbanowicz, On diophantine equations involving sums of powers with quadratic characters as coefficients, II
- Janusz Szmidt, Jerzy Urbanowicz, Don Zagier, Congruences among generalized Bernoulli numbers

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