Struggling with Describing a Riemann Surface for log(z2 - za)?

Thread starter wofsy
Start date Jan 8, 2010
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Riemann Surface

In summary, Riemann surfaces are mathematical objects that extend the complex plane to a higher dimensional space. They are important in many areas of mathematics and are commonly used in physics to study complex systems. Some examples of Riemann surfaces include the Riemann sphere and the torus, and there are various resources available for learning more about them. A strong background in complex analysis and topology is also helpful in understanding Riemann surfaces.

Jan 8, 2010

wofsy

I am having trouble describing the Riemann surface of log(z) + log(z-a)

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Jan 9, 2010

mathman

Science Advisor

I am very rusty on this subject, but did you try working with the combined log ?
[log(z² - za)]

Last edited: Jan 9, 2010

Related to Struggling with Describing a Riemann Surface for log(z2 - za)?

1. What is a Riemann surface?

A Riemann surface is a mathematical concept that extends the complex plane to a higher dimensional space. It is a type of manifold that allows for complex numbers to be represented as points on a surface, rather than just on a plane.

2. Why are Riemann surfaces important?

Riemann surfaces are important in many areas of mathematics, including complex analysis, algebraic geometry, and topology. They provide a way to study complex functions and algebraic curves in a geometric framework, making it easier to visualize and understand these concepts.

3. How are Riemann surfaces used in physics?

In physics, Riemann surfaces are used to study phenomena in quantum mechanics, string theory, and general relativity. They provide a way to understand the behavior of particles and fields in complex systems and curved spacetime.

4. What are some common examples of Riemann surfaces?

Some common examples of Riemann surfaces include the Riemann sphere, the complex projective line, and the torus. These surfaces can also be classified by their genus, which is a measure of the number of "holes" in the surface.

5. How can I learn more about Riemann surfaces?

There are many resources available for learning about Riemann surfaces, including textbooks, online courses, and lectures. It is also helpful to have a strong background in complex analysis and topology. Additionally, working with a mentor or taking a class on the subject can provide a deeper understanding of Riemann surfaces.