Lecture

Fourier Expansion and Modular Forms

Related lectures (28)

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.

Delves into the construction and optimality of the E8 lattice as the densest sphere packing in dimension eight.

Explores de Rham theory, L-values, and extensions, including special value formulas and examples related to Hecke characters and modular forms.

Explores the Monster group, a sporadic simple group with a unique representation theory.

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

Explores matrix operations, trends, and convergence conditions with a focus on clear definitions and examples.

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.

Explores Dirichlet series convergence properties and absolute convergence conditions, with examples and applications.

Explores limits, convergence, and boundedness of functions and sequences.