Canonical Divisors and Modular Forms

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

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

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

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

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

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

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

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

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

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