I'm trying to write a program that plots the riemann zeta function

In summary, When researching, the speaker saw a picture that showed complex coordinates becoming darker as their value increased, resulting in a helpful graph. However, the speaker is unsure of the scale used in the picture. When creating their own program, the speaker divided the result of the function by 10000 and used that number to set the darkness of the point, with 0 being the darkest and 255 being the brightest. This resulted in a graph that was somewhat similar to the ideal one, but not very accurate. The graph had a slightly curved line going down around the imaginary axis, with a few brighter spots near it at regular intervals of about 5 units. The speaker asks for advice on what scale to use when translating the function's
  • #1
LastTimelord
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I saw a picture of what it might look like when I was researching it, but I'm confused about something. The picture's caption said that the complex coordinates were darkened as their value got larger, leading to a helpful graph, but I do not understand what scale they used. For my program, I just divided the result of the function by 10000, then used that number to set the darkness of the point, 0 being the darkest and 255 being the brightest. That resulted something that looked remotely similar to the ideal graph, but it really wasn't very decent. There was a slightly curved line going down around the imaginary axis, with a few brighter spots near it going down at regular intervals of about 5 units. (I'm sorry I don't have a picture, but it would be hard to get one).

Anyway- to the question:

What scale do you think I should use to translate the number returned from the function to darkness? Should it be logarithmic, or linear?
 
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  • #2
This depends on your goal. A logarithmic scale emphasizes the low values, a linear scale is closer to the actual data. Such things are defined by the goal, not by the method.
 

1. What is the Riemann Zeta Function?

The Riemann Zeta Function is a mathematical function that was first introduced by the mathematician Bernhard Riemann in the 1850s. It is defined as the sum of the reciprocals of the positive integers raised to a given power. The function is denoted by the symbol ζ and is widely used in number theory and other areas of mathematics.

2. Why is the Riemann Zeta Function important?

The Riemann Zeta Function is important because it has connections to many important areas of mathematics, including number theory, complex analysis, and physics. It is also closely related to the distribution of prime numbers and the distribution of zeros of the Riemann Zeta Function has been a subject of much research and conjecture.

3. How is the Riemann Zeta Function computed?

The Riemann Zeta Function can be computed using a variety of methods, including numerical approximations, series expansions, and functional equations. One common method is to use Euler-Maclaurin summation to approximate the function for a given number of terms. There are also many specialized algorithms and computer programs that can compute the Riemann Zeta Function more efficiently.

4. What is the significance of plotting the Riemann Zeta Function?

Plotting the Riemann Zeta Function can help visualize the behavior of the function and its relationship to other mathematical concepts. It can also be used to study the distribution of zeros and identify potential patterns or structures. Additionally, plotting the function can be a useful tool for teaching and understanding the properties of the Riemann Zeta Function.

5. Are there any challenges in writing a program to plot the Riemann Zeta Function?

Yes, there are several challenges in writing a program to plot the Riemann Zeta Function. One challenge is dealing with the infinite series involved in the function and finding ways to approximate it. Another challenge is ensuring accuracy and efficiency in the program, especially for large values of the input. Additionally, the complexity and behavior of the function may make it difficult to identify potential errors or bugs in the program.

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