The work of Gross and Zagier on Heegner points and the derivatives of L -series

John Coates

Séminaire Bourbaki (1984-1985)

  • Volume: 27, page 57-72
  • ISSN: 0303-1179

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Coates, John. "The work of Gross and Zagier on Heegner points and the derivatives of $L$-series." Séminaire Bourbaki 27 (1984-1985): 57-72. <http://eudml.org/doc/110052>.

@article{Coates1984-1985,
author = {Coates, John},
journal = {Séminaire Bourbaki},
keywords = {Heegner point; height-pairing; L-series; elliptic curves; class number problem},
language = {eng},
pages = {57-72},
publisher = {Société Mathématique de France},
title = {The work of Gross and Zagier on Heegner points and the derivatives of $L$-series},
url = {http://eudml.org/doc/110052},
volume = {27},
year = {1984-1985},
}

TY - JOUR
AU - Coates, John
TI - The work of Gross and Zagier on Heegner points and the derivatives of $L$-series
JO - Séminaire Bourbaki
PY - 1984-1985
PB - Société Mathématique de France
VL - 27
SP - 57
EP - 72
LA - eng
KW - Heegner point; height-pairing; L-series; elliptic curves; class number problem
UR - http://eudml.org/doc/110052
ER -

References

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  1. [1] B. Birch.- Diophantine analysis and modular functions, Proceedings of Bombay Colloquium on Algebraic Geometry (1968), 35-42. Zbl0246.10017MR258832
  2. [2] B. Birch.- Elliptic curves and modular functions, Symposia Mathematica (1970), 27-32. Zbl0225.14016MR269654
  3. [3] B. Birch.- Heegner points of elliptic curves, Symposia Mathematica (1975), 441-445. Zbl0317.14015MR384805
  4. [4] B. Birch and N. Stephens.- Heegner's construction of points on the curve y2 = x3 - 1728e3, Progress in Mathematics Vol. 38 (1983), 1-19. Zbl0535.14012MR729156
  5. [5] J. Cassels and A. Bremmer.- On the equation y2 = x (x2+p) , Math. of Computation Vol. 42 (1984), 257-264. Zbl0531.10014MR726003
  6. [6] B. Gross.- Heegner points on X0(N), to appear in Proceedings of the Durham Conference on Modular Forms (1983). Zbl0559.14011MR803364
  7. [7] B. Gross.- Local Heights on Curves, to appear in Proceedings of the Storrs Conference on Algebraic Geometry (1984). Zbl0605.14027MR861983
  8. [8] B. Gross and D. Zagier.- Points de Heegner et dérivées de fonctions L, CRAS297 (1983), 85-87. Zbl0538.14023MR720914
  9. [9] B. Gross and D. Zagier.- Heegner points and derivatives of L-series, to appear in Invent. Math. Zbl0608.14019MR833192
  10. [10] E. Hecke.- Zur Theorie der elliptischen Modulfunktionen, Math. Werke, 428- 460. JFM52.0377.04
  11. [11] K. Heegner.- Diophantische Analysis und Modulfunktionen, Math. Zeitschrift56 (1952), 227-253. Zbl0049.16202MR53135
  12. [12] A. Néron.- Quasi-fonctions et hauteurs sur les variétés abéliennes, Ann. of Math.82 (1965), 249-331. Zbl0163.15205MR179173
  13. [13] J. Tate.- The arithmetic of elliptic curves, Invent. Math.23 (1974), 179- 206. Zbl0296.14018MR419359
  14. [14] J.-L. Waldspurger. - Correspondance de Shimura et Quaternions, to appear. Zbl0567.10020MR1103429
  15. [15] Whittaker and Watson.- Modern Analysis, Cambridge University Press (4th edition) (1952). 
  16. [16] A. Atkin and J. Lehner.- Hecke operators on Γ0(m), Math. Ann. Vol. 185 (1970), 134-160. Zbl0177.34901

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