Lectures related to Modular Lambda Function: Properties and Applications

Explores essential chief series in tdlc groups, focusing on closed, normal subgroups and their chief factors.

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

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

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

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

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores uniform convergence of series of functions and its significance in complex analysis.

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

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

Explores holomorphic functions in complex analysis and the Cauchy-Riemann equations.

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Explores holomorphic functions, Cauchy-Riemann conditions, and principal argument values in complex analysis.

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

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

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

Covers the Cauchy-Riemann conditions and potential functions in complex analysis.

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

Covers the fundamentals of complex analysis, focusing on complex functions, their properties, and applications in solving differential equations.

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