Tópicos de Formas Modulares e Curvas Elípticas

Pré-requisito: Análise Complexa

Modular and congruence groups, modular forms of a given weight, cusp forms, Eisenstein series, theta series, Weierstrass pi function, elliptic curves in Weierstrass format, elliptic curves as group, rank of elliptic curves, Mordell-Weil theorem, Hecke operators, Fourier expansions, Growth of the coefficients, L-functions of modular forms and elliptic curves, Birch Swinnerton-Dyer conjecture, functional equation of L-functions, Old forms and new forms, modular elliptic curves, Galois representations and modular forms, application to congruent numbers, Arithmetic modularity of elliptic curves and its relation with Fermat’s last theorem.

KOBLITZ, NEAL,  Introduction to elliptic curves and modular forms, Graduate Texts in Mathematics, 97. Springer-Verlag, New York, 1993.
SLVERMAN, JOSEPH H., Advanced topics in the arithmetic of elliptic curves. Graduate Texts in Mathematics, 151. Springer-Verlag, New York, 1994.
SLVERMAN, JOSEPH H., The arithmetic of elliptic curves. Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1992.
DIAMOND, FRED; SHURMAN, JERRY., A first course in modular forms. Graduate Texts in Mathematics, 228. Springer-Verlag, New York, 2005.
DALE HUSEMOLLER, Elliptic curves, volume 111, Graduate Texts in Mathematics, Springer-Verlag, New York, second edition, 2004.
ZAGIER, D., Elliptic modular forms and their applications, Universitext, Springer, 2008.
LANG, S., Introduction to modular forms, Grund. Math. Wiss. 222, springer, 1995.