586 XIII Connections with Number Theory
[50] J.H. Silverman,The arithmetic of elliptic curves, Springer-Verlag, New York, 1986.
[51] J.H. Silverman,Advanced topics in the arithmetic of elliptic curves, Springer-Verlag,
New York, 1994.
[52] J.H. Silverman and J. Tate,Rational points on elliptic curves, Springer-Verlag, New York,
1992.
[53] L. Szpiro, La conjecture de Mordell [d’apr`es G. Faltings],Ast ́erisque121–122(1985),
83–103.
[54] J.T. Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog,
S ́eminaire Bourbaki: Vol. 1965/1966, Expos ́e no. 306, Benjamin, New York, 1966.
[55] J.T. Tate, The arithmetic of elliptic curves,Invent. Math. 23 (1974), 179–206.
[56] R.L. Taylor and A. Wiles, Ring theoretic properties of certain Hecke algebras,Ann. of
Math. 141 (1995), 553–572.
[57] J.B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2,Invent.
Math. 72 (1983), 323–334.
[58] N. Ja. Vilenkin and A.V. Klimyk,Representation of Lie groups and special functions,
4 vols., Kluwer, Dordrecht, 1991–1995.
[59] M. Waldschmidt,Diophantine approximation on linear algebraic groups, Springer,
Berlin, 2000.
[60] A. Wiles, Modular elliptic curves and Fermat’s last theorem,Ann. of Math. 141 (1995),
443–551.
AdditionalReferences
R.E. Borcherds, What is moonshine?,Proceedings of the International Congress
of Mathematicians: Berlin 1998, Vol. I, pp. 607–615, Documenta Mathematica,
Bielefeld, 1998.
C. Breuil, B. Conrad, F. Diamond and R. Taylor, On the modularity of elliptic curves
over Q,J. Amer. Math. Soc. 14 (2001), 843–939.
Chandrasekhar Khare, Serre’s modularity conjecture,Preprint.