MA 215: Introduction to Modular Forms

Credits: 3:0

Pre-requisites :

1. MA 224 (Complex Analysis) or equivalent

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.

Suggested books and references:

1. Serre, J.P., A Course in Arithmetic, Graduate Texts in Mathematics no. 7, Springer-Verlag, 1996.
2. Koblitz, N., Introdution to Modular Forms, Graduate Texts in Mathematics no. 97, Springer-Verlag, 1984.
3. Iwaniec, H., Topics in Classical Automorphic Forms, Graduate Texts in Mathematics 17, AMS, 1997.
4. Diamond, F. and Schurman, J., A First Course in Modular Forms, Graduate Texts in Mathematics no. 228, Springer-Verlag, 2005.

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