Pathway XXIV

ΓModular forms

Functions on the upper half-plane, invariant under SL₂(ℤ) up to a weight factor.

1. 01The modular groupSL₂(ℤ) acts on the upper half-plane by fractional linear maps. A fundamental domain is a single tile.4 min
2. 02q-expansionsA modular form is determined by its Fourier series at the cusp: ∑ aₙ qⁿ, q = e^{2πiτ}.4 min