Program for graphing Riemann zeta function

In summary, the program has been fixed and should be calculating correct (or at least more correct) values now.
  • #1
donotremember
31
0
Hello I plan on applying to the university of waterloo next year and due to the fact that many of my marks are not that great (failed gr 10 math) I decided to start a site to showcase my ability in math and programing.

For those of you who are interested I wrote a program to graph regions of the Riemann zeta function which you can find here:

donotrememberthisaddress.com/mathematics/zetafunctionviewer.php

I also give a short description of what the Riemann hypothesis means which you find here:

donotrememberthisaddress.com/mathematics/whatisriemannhypothesis.php

as well as how to calculate a value of the zeta function:

donotrememberthisaddress.com/mathematics/calculatevalue.php

I welcome you to point any mistakes that I may have made and also encourage you to check out the main page if you like as I list several resources for finding free video lectures and information.
 
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  • #2
Note: I recompiled the zeta function viewer program with static linking so that it no longer generates an error complaining about the program configuration being incorrect.
 
  • #3
Just to let anyone know who downloaded the program before I screwed up in the calculation of zeta function so any input values for zeta with an imaginary part will were wrong.

I thougth it was working because all the values with only real parts checked out to be ok and I was able to calculate some of the zeros correctly.

I have not been able to find a source that says gives some examples of what correct output for complex input values should be so I have had to rely on a graph of the real and imaginary part on just the real critical line and see if they look like they are prety close.



The program has been fixed and should be calculating correct (or at least more correct) values now.
 
  • #4
donotremember said:
Just to let anyone know who downloaded the program before I screwed up in the calculation of zeta function so any input values for zeta with an imaginary part will were wrong.

I thougth it was working because all the values with only real parts checked out to be ok and I was able to calculate some of the zeros correctly.

I have not been able to find a source that says gives some examples of what correct output for complex input values should be so I have had to rely on a graph of the real and imaginary part on just the real critical line and see if they look like they are prety close.



The program has been fixed and should be calculating correct (or at least more correct) values now.
For those who decline to look at your program. Why not post some of the results of the program so others can check the accuracy as compared with the expensive and out of reach programs for me? Also what corrections did you make to get the current results?

PS I got a few F's occasionally in math but also many A's. I could do the work but sometimes didn't make the effort. Don't take the easy way and settle on a program of study or career that doesn't suit your interests like I did. Even if you are not accepted now stay with your dreams and make them come true. I found myself in a career that paid well but failed to work towards my real interests and wasn't ready to take the opportunity to change careers, i.e. get into computer programming, when the chance came. A retired patent examiner.
 
  • #5
ramsey2879 said:
For those who decline to look at your program. Why not post some of the results of the program so others can check the accuracy as compared with the expensive and out of reach programs for me? Also what corrections did you make to get the current results?

I was messing around trying to figure out what the period of a pattern I noticed was in the zeta function and found that my calculations on paper did not agree with what the program told me. I then reviewed my code and found that when calculating the real part I overwrote a variable that I needed to calculate the Imaginary part making the imaginary values wrong. This was fixed by introducing a couple more variables.

Here are some calculations made by my program using the first 10000 iterations:

zeta(3 + i0) = 1.202057 + i0

zeta(3 + i0.1) = 1.200861 - i0.019750

zeta(0.5 + i33) = -0.044787 + i0.081399

zeta(1 + i33) = 0.418661 + i0.0244871

zeta(1 + i123456789) = 0.274378 - i0.582564
 

1. What is the Riemann zeta function?

The Riemann zeta function is a mathematical function that is used to study the distribution of prime numbers. It is named after mathematician Bernhard Riemann and is defined as the sum of the reciprocals of all positive integers raised to a given power. The Riemann zeta function is denoted by the symbol ζ(s) and is a complex function.

2. Why is the Riemann zeta function important?

The Riemann zeta function is important because it is closely related to the distribution of prime numbers. It has many applications in number theory, including the famous Riemann hypothesis which states that all non-trivial zeros of the Riemann zeta function lie on a specific line in the complex plane. Additionally, the Riemann zeta function is also used in physics, specifically in the study of quantum chaos.

3. What is the significance of graphing the Riemann zeta function?

Graphing the Riemann zeta function allows us to visualize its behavior and explore its properties. It can help us gain a better understanding of the distribution of prime numbers and potentially provide insights into proving the Riemann hypothesis. Furthermore, graphing the Riemann zeta function can also reveal interesting patterns and connections with other mathematical functions.

4. How is the Riemann zeta function graphed?

The Riemann zeta function can be graphed in various ways, depending on the purpose and the range of values being considered. One common method is to plot the values of the function for a range of complex numbers on the complex plane, resulting in a three-dimensional plot. Another approach is to use contour plots, which show curves of equal values on the complex plane. There are also programs available that can generate interactive graphs of the Riemann zeta function.

5. What are some practical applications of graphing the Riemann zeta function?

Aside from its importance in number theory and physics, graphing the Riemann zeta function can also have practical applications in engineering and computer science. For example, it can be used in the design of efficient algorithms for factoring large numbers, which has important implications for cryptography. Additionally, graphing the Riemann zeta function can also aid in the analysis and optimization of signal processing systems, such as filters and equalizers.

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