Geodesic
The rank of J 0 (N)
Columbia university number theory seminar - New-York, 1992, Astérisque, no. 228 (1995), pp. 41-68

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Brumer, Armand. The rank of $J_0(N)$, dans Columbia university number theory seminar - New-York, 1992, Astérisque, no. 228 (1995), pp. 41-68. http://geodesic.mathdoc.fr/item/AST_1995__228__41_0/

1. A. O. L. Atkin and J. Lehner. Hecke operators on Γ 0 (m). Math. Ann. 185 134-160 (1970).

2. A. O. L. Atkin and W. Li. Twists of new forms and pseudo-eigenvalues of W-operators, Math. Ann. 185 134-160 (1970).

3. B. Birch. Hecke actions on classes of ternary quadratic forms. in Computational Number Theory, a conference, 1989).

4. B. Birch and W. Kuyk (eds). Modular functions of one variable, Lecture Notes in Mathematics 476, Springer-Verlag, New-York, 1975.

5. S. Böcherer and R. Schulze-Pillot. Siegel modular forms and theta series attached to quaternion algebras, Nagoya Jl. of Mathematics 121 35-96 (1991).

6. A. Brumer. The average rank of elliptic curves I, Inv. Math. 109, 445-472 (1992).

7. A. Brumer. Curves with real multiplications, (in preparation).

8. A. Brumer and R. Heath-Brown. The average rank of elliptic curves II, (in preparation).

9. A. Brumer and K. Kramer. The conductor of abelian varieties, (to appear in Compos. Math.). | MR | Zbl | EuDML | Numdam

10. A. Brumer and O. Mcguinness. The behavior of the Mordell-Weil group of elliptic curves, Bull. AMS 23 375-381 (1990). | MR | Zbl | DOI

11. D. Bump, S. Friedberg and J. Hoffstein, Nonvanishing theorems for L-functions of modular forms and their derivatives, Inv. Math. 102 543-618 (1990). | MR | Zbl | EuDML | DOI

12. J. E. Cremona. Algorithms for modular elliptic curves, Cambridge Univ. Press (1992). (1990). | MR | Zbl

13. B. Gross. Heights and the special values of L-series, in Can. Math. Soc. Conf. Proc. 7 (1989). | MR | Zbl

14. B. Gross and D. Zagier. Heegner points and derivatives of L-series, Inv. Math. 84 225-320 (1986). | MR | Zbl | EuDML | DOI

15. A. Grothendieck. Modèles de Néron et monodromie, SGA 7, Exposé IX, Springer Lecture Notes 288 313-523, Springer-Verlag, New-York. | Zbl

16. G. H. Hardy and E. M. Wright. Introduction to the theory of numbers, 3rd ed., Oxford (1954). | MR | Zbl

17. A. Hurwitz. Ueber Relationen zwischen Klassenzahlen binärer quadratischer Formen von negativer Determinante, Math. Ann. 25 157-196 (1885). | MR | JFM | EuDML | DOI

18. V. A. Kolyvagin and D. Y. Logachev. Finiteness of the Shafarevich-Tate group and the group of rational points for some modular abelian varieties, Leningrad Math. Jl. 1 (1990). | MR | Zbl

19. J. Kramer. On the linear independence of certain theta series, Math. Ann. 281 219-228 (1988). | MR | Zbl | EuDML | DOI

20. B. Mazur. Modular curves and the Eisenstein ideal, Publ. Math. I.H.E.S. 47 33-186 (1977). | MR | Zbl | EuDML | Numdam | DOI

21. J.-F. Mestre. Formules explicites et minorations de conducteurs de variétés algébriques, Compos. Math. 58 209-232 (1982). | MR | Zbl | Numdam | EuDML

22. J.-F. Mestre and J. Oesterlé. Courbes de Weil fortes de conducteur premier <14000, (Unpublished). | Zbl

23. M. R. Murty, V. K. Murty. Mean values of derivatives of modular L-series, Preprint (1989). | MR | Zbl

24. K. Ribet. Endomorphisms of semi-stable abelian varieties over number fields, Annals of Math. 101 555-562 (1975). | MR | Zbl | DOI

25. K. Ribet. Galois actions on division points of abelian varieties with many real multiplications, Amer. Jl. of Math. 98 751-804 (1976). | Zbl | MR | DOI

26. K. Ribet. Abelian varieties over ℚ and modular forms, preprint (1992). | Zbl | MR

27. H. Saito. On a decomposition of spaces of cusp forms and trace formula Hecke operators, Nagoya Jl. of Math. 80 129-165 (1980). | MR | Zbl | DOI

28. J.-P. Serre. Quelques applications du théorème de densité de Chebotarev, Publ. Math. I.H.E.S. 47 323-201 (1981). | Zbl | EuDML | Numdam

29. J.-P. Serre. Sur les représentations modulaires de degré 2 de Gal(ℚ ¯/ℚ), Duke Math. Jl. 54 179-230 (1987). | MR | Zbl | DOI

30. J.-P. Serre. Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C.R. Acad Sci. Paris 296 397-402 (1983). | MR | Zbl

31. G. Shimura. Introduction to the theory of automorphic functions. Princeton, 1971. | Zbl | MR

32. N.-P. Skoruppa and D. Zagier. Jacobi forms and a certain space of modular forms, Inv. Math. 94 113-146 (1988). | MR | Zbl | EuDML | DOI