Modular forms: Theta functions in higher dimensions @richarde.borcherds7998

Uploaded March 2021 | Updated September 2026, 2 weeks ago

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

We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot "her the shape of a drum", and calculate the number of minimal vectors in the Leech lattice, and show that any even unimodular lattice has to have dimension divisible by 8.

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

Modular forms: Theta functions in higher dimensions

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