Fourier Expansion and Modular Forms

Related lectures (28)

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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.