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.

Referências:
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.