By the end of this course, a student will:
- make computations regarding modular forms and functions using their complex analytic description,
- work with the description of modular forms and functions as meromorphic forms and functions on the moduli space of elliptic curves with additional structure,
- compute dimensions of spaces of modular forms using the Riemann-Roch theorem,
- deduce number theoretical results using the dimension formulae,
- understand the role of Hecke operators in the theory,
- understand the statement of the Taniyama-Shimura-Weil conjecture from different perspectives, and its relation to Fermat’s last theorem.