**Program**:

- 1. Modular groups, modular functions, modular forms. Fundamental domains. Finite dimensionality of spaces of modular forms.
- 2. Eisenstein series, the discriminant.
- 3. Theta-series.
- 4. Hecke eigenseries and L-series.
- 5. Differential operators: derivatives of modular forms, Rankin-Cohen brackets, quasi-modular forms.
- 6. Complex multiplication.

we loosely follow Don Zagier’s book with same name.

Zagier, Don. "Elliptic modular forms and their applications." The 1-2-3 of modular forms. Springer Berlin Heidelberg, 2008. 1-103.

**When & Where**: Jan-Feb 2023, PUC-Rio

Ementa em português,

Extended syllabus and Teaser

Last time read: 2015.1 @ HSE