(All images created with MATLAB® software)

Click on pictures for more information and an image of higher resolution.

Figure 1: Riemann Surface of the function f(z)=log(z^{2}-1)

To construct the **Riemann Surface for the function f(z)=log(z ^{2}-1)**, we start with the complex plane with two cuts along the real axis: one for x > 1 and the other for x < -1. Here the function has infinitely many branches. Then we proceed in the same fashion used in the previous examples.

**The two pictures show two views of the resulting surface**. We note that this

**Riemann Surface is an object in three dimensional space**. Furthermore, this is an example with

**three branch points**, in which it differs from all the prior examples (which only had two branch points).

**The branch points are z=1, z=2 and infinity**.

Figure 2: Top view for the Riemann Surface of the function f(z)=log(z^{2}-1)