### MA 215: Introduction to Modular Forms

#### 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 :

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.

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in