Introduction to Modular Forms The modular group and its subgroups, the fundamental domain. Modular forms, examples, Eisenstein series, cusp forms. Valence (dimension) formula, Petersson inner product. Hecke operators. L-functios: definition, analytic continution and functional equation. Recommended books
- Serre, J.P., A Course in Arithmetic, Graduate Texts in Mathematics no. 7 Springer-Verlag, 1996.
- Koblitz, N., Introdution to Modular Forms, Graduate Texts in Mathematics no. 97, Springer-Verlag, 1984.
- Iwaniec, H., Topics in Classical Automorphic Forms, Graduate Texts in Mathematics 17, AMS, 1997.
- Diamond, F. and Schurman, J., A First Course in Modular Forms, Graduate Texts in Mathematics no. 228, Springer-Verlag, 2005.
PREREQUISITES:
MA 224 (Complex Analysis) or equivalent