Uploaded March 2021 | Updated September 2026, 1 week ago

---

This lecture is part of an online graduate course on modular forms.

We classify all meromorphic modular functions, showing that they are all rational functions of the elliptic modular function j.

As an application of j we use it to prove Picard's theorem that a non-constant meromorphic function can omit at most one value.

For the other lectures in the course see youtube.com/playlist?list=PL8yHsr3EFj51HisRtNyzHX-Xyg6I3Wl2F