In complex theory of functions one studies differentiable mappings into the complex numbers.

Riemann surfaces

A Riemann surface is a one dimensional complex manifold. The easiest examples is the complex plane \(\mathbb{C}\).

Conformal maps

A conformal mapping is an angle-preserving mapping.

Real and imaginary parts of some functions

Automorphic functions

An automorphic function is an analytic function, which is invariant under certain transformation. Elliptic functions are automorphic functions with double period.

Surfaces and charts of the absolute value of some functions

Elliptic functions

Elliptic functions are automorphic functions with double period.