Modular Forms: Dimension Formulas

Related lectures (31)

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Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Explores meromorphic differentials on Riemann surfaces and modular forms on congruence subgroups.

Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.

Explores the properties and transformations of theta functions, including modular forms and lattice levels.

Covers canonical divisors on Riemann surfaces and properties of modular forms.

Explores holomorphic maps, ramification points, and the genus of a modular curve.

Covers the Fourier expansion of modular forms and the Rankin-Selberg method.

Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.

Covers the Petersson inner product and Hecke operators in modular forms theory, exploring their definitions and properties.