Geodesic
Elliptic Curves and Modular Forms
Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 375-384

Voir la notice de l'article provenant de la source Cambridge University Press

This is a survey of some recent developments in the theory of elliptic curves. After an informal discussion of the main theorems of the arithmetic side of the theory and the open problems confronting the subject, we describe the recent work of K. Rubin, V. Koly vagin, K. Murty and the author which establishes the finiteness of the Shafarevic-Tate group for modular elliptic curves of rank zero and one.
DOI : 10.4153/CMB-1991-060-4
Mots-clés : 11G05, 11G40 
Murty, M. Ram. Elliptic Curves and Modular Forms. Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 375-384. doi: 10.4153/CMB-1991-060-4
@article{10_4153_CMB_1991_060_4,
     author = {Murty, M. Ram},
     title = {Elliptic {Curves} and {Modular} {Forms}},
     journal = {Canadian mathematical bulletin},
     pages = {375--384},
     year = {1991},
     volume = {34},
     number = {3},
     doi = {10.4153/CMB-1991-060-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-060-4/}
}
TY  - JOUR
AU  - Murty, M. Ram
TI  - Elliptic Curves and Modular Forms
JO  - Canadian mathematical bulletin
PY  - 1991
SP  - 375
EP  - 384
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-060-4/
DO  - 10.4153/CMB-1991-060-4
ID  - 10_4153_CMB_1991_060_4
ER  - 
%0 Journal Article
%A Murty, M. Ram
%T Elliptic Curves and Modular Forms
%J Canadian mathematical bulletin
%D 1991
%P 375-384
%V 34
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-060-4/
%R 10.4153/CMB-1991-060-4
%F 10_4153_CMB_1991_060_4

[1] 1. Bump, D., S. Friedberg and Hoffstein, J., Non-vanishing theorems for L-functions of modular forms and their derivatives, Invent. Math. 102 (1990), 543–618. Google Scholar

[2] 2. Gross, B. and Zagier, D., Heegner points and derivatives of L-series, Invent. Math. 84 (1986), 225–320. Google Scholar

[3] 3. Koly, V. A. vagin, Finiteness ofE(Q) and l\lE/ Q for a subclass of Weil curves, Izv. Akad. Nauk. SSSR Ser. Math. 52 (1988), 522–540; English transi, in Math. USSR Izv. 32(1989). Google Scholar

[4] 4. Ram Murty, M., On simple zeroes of certain L-series , in Number Theory, Proceedings of the Banff conference, (ed. R. Mollin), 1990,427-439, Walter de Gruyter. Google Scholar

[5] 5. Ram, M. Murty, and V. Kumar Murty, Mean values of derivatives of modular L-series, Annals of Mathematics, 133 (1991), 447–475. Google Scholar

[6] 6. Rubin, K., Tate-Shafarevic groups and L-functions of elliptic curves with complex multiplication, In v. Math. (3)89 (1987), 527–559. Google Scholar

[7] 7. Silverman, J., The arithmetic of elliptic curves. Springer-Verlag, New York, 1986. Google Scholar

Cité par Sources :