Nombres de classes des corps quadratiques imaginaires

Joseph Oesterlé

Séminaire Bourbaki (1983-1984)

  • Volume: 26, page 309-323
  • ISSN: 0303-1179

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Oesterlé, Joseph. "Nombres de classes des corps quadratiques imaginaires." Séminaire Bourbaki 26 (1983-1984): 309-323. <http://eudml.org/doc/110032>.

@article{Oesterlé1983-1984,
author = {Oesterlé, Joseph},
journal = {Séminaire Bourbaki},
keywords = {elliptic curves; class numbers; imaginary quadratic fields; form with rational coefficients; L-series; high order zero},
language = {fre},
pages = {309-323},
publisher = {Société Mathématique de France},
title = {Nombres de classes des corps quadratiques imaginaires},
url = {http://eudml.org/doc/110032},
volume = {26},
year = {1983-1984},
}

TY - JOUR
AU - Oesterlé, Joseph
TI - Nombres de classes des corps quadratiques imaginaires
JO - Séminaire Bourbaki
PY - 1983-1984
PB - Société Mathématique de France
VL - 26
SP - 309
EP - 323
LA - fre
KW - elliptic curves; class numbers; imaginary quadratic fields; form with rational coefficients; L-series; high order zero
UR - http://eudml.org/doc/110032
ER -

References

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  5. [C 11] M.K. Agrawal, J.H. Coates, D.C. Hunt and J.A. van der Poorten - Elliptic curves of conductor 11, Math. of Comp.35(1980), 991-1002. Zbl0475.14031MR572871
  6. [De] P. Deligne - Preuve des conjectures de Tate et Shafarevitch (d'après G. Faltings), Séminaire Bourbaki, exp. 616, novembre 1983, Astérisque n° 121-122(1985), 25-41. Zbl0591.14026MR768952
  7. [Ga] C.F. Gauss - Disquisitiones arithmeticae, Werke, t. I. 
  8. [G,J] S. Gelbart and H. Jacquet - A relation between automorphic representations of GL(2) and GL(3), Ann. Sci. E.N.S. (4) 11(1978), 471-542. Zbl0406.10022MR533066
  9. [G,Z] B. Grdss et D. Zagier - Points de Heegner et dérivées de fonctions L, C.R. Acad. Sc. Paris297(1983), 85-87. Zbl0538.14023MR720914
  10. [He] K. Heegner - Diophantische Analysis und Modulfunktionen, Math. Z.56(1952), 227-253. Zbl0049.16202MR53135
  11. [Hei] H. Heilbrdnn - On the class-number in imaginary quadratic fields, Quarterly J. of Math. (Oxford)5(1934), 150-160. Zbl0009.29602JFM60.0155.01
  12. [Go] D.M. Goldfeld - The conjectures of Birch and Swinnerton-Dyer and the class numbers of quadratic fields, Journées Arithmétiques de Caen, Astérisque41- 42(1977), 219-227. Zbl0355.12005MR447176
  13. [M,S-D] B. Mazur and P. Swinnerton-Dyer - Arithmetic of Weil Curves, Invent. Math.25(1974), 1-61. Zbl0281.14016MR354674
  14. [M,W] H.L. Montgomery and P.J. Weinberger - Notes on small class numbers, Acta Arithmetica24(1973), 529-542. Zbl0285.12004MR357373
  15. [Oe] J. Oesterlé - Résolution effective du problème du nombre de classes des corps quadratiques imaginaires, à paraître. 
  16. [Ogg] A.P. Ogg - On a convolution of L-series, Invent. Math.7(1969), 297-312. Zbl0205.50902MR246819
  17. [Sh] G. Shimura - On the holomorphy of certain Dirichlet series, Proc. of the London Math. Soc.31(1975), 79-98. Zbl0311.10029MR382176
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  20. [St 1] H.M. Stark - There is no tenth complex quadratic field with class-number one, Proc. Nat. Acad. Sci. U.S.A.57(1967), 216-221. Zbl0148.27803MR211984
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Citations in EuDML Documents

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  1. Olivier Ramaré, A purely analytical lower bound for L ( 1 , χ )
  2. Bruno Harris, An analytic function and iterated integrals
  3. Steven Arno, The imaginary quadratic fields of class number 4
  4. Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number
  5. Ken Ono, Lawrence Sze, 4-core partitions and class numbers
  6. Ken Yamamura, Maximal unramified extensions of imaginary quadratic number fields of small conductors
  7. Ben Kane, CM liftings of supersingular elliptic curves
  8. Pierre Colmez, La conjecture de Birch et Swinnerton-Dyer 𝐩 -adique

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