Fourier Expansion and Modular Forms

Related lectures (28)

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

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

Covers dimension formulas for modular forms and related proofs using Riemann-Roch corollaries.

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

Delves into the representation of SL2Z and the function F, exploring its transformation properties and relation to modular forms.

Covers the properties and applications of modular forms and discusses equidistribution and modularity.

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Explores extremal lattices, emphasizing bounds on shortest vectors and unique modular forms.

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

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