Lectures related to Modular Forms: Dimension Formula

Covers linear independence, bases, and coordinate systems with examples and theorems.

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

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

Explores the Cauchy-Riemann equations, holomorphic functions, and the integral formula of Cauchy.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

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

Discusses Laurent series, residue theorem, and their applications in complex analysis.

Provides an overview of complex analysis, focusing on derivatives, integrals, and the Cauchy theorem.

Introduces complex analysis, focusing on holomorphic functions and the Cauchy-Riemann equations.