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What is Divisor Wave Prime Complex Analysis?

These waveforms breakdown the structure of prime numbers and represent them in a new light, the Divisor Wave Prime Complex Analysis plotting software is an infinite domain which I have defined for researching these special functions. Ultimately this software contains infinitely many functions which I have not gotten the opportunity to explore, and because of this I invite you to join me in transversing the complex plane for discrete product series, and there relationship to primes, chaos, order, and mathematics.

Downloading the PDF File:

For full comprehension of the software please read PDF version of the research paper which is located in the repository under the folder PDF_Files Please either pulldown/download the entire repository for Divisor Wave Prime Complex Analysis or Navigate to the PDF file in the repository to read the paper, pdf file named: Divisor_Waves_and_their_Connection_to_the_Riemann_Hypothesis.pdf

I have been working hard on these proofs for the past 4 years and now with the advent of ChatGPT which can be tasked with automating the convertion of data types, leveraging this I have had an explosive amount of research opportunities given the swiftness of implementation. The Divisor Wave Prime Complex Analysis Plotting software is free and open source, and encourages development by users. Given the environment users can create and research new formulas in the complex space of product series allowing anyone to find novel functions in an uncharted territory.

Divisor-Wave-Prime-Complex-Analysis

A program for plotting complex functions. This tool provides the plotting functions for 2D and 3D graphics for infinite series such as the Riemann zeta function, the infinite product of the product representation for sin(pi*z/n) as well as any other function that can be formulated in the complex plane. The Infinite product plotted throughout the paper known as b(z) acts as an indicator for prime and composite numbers. ultimately we can describe a complex product waveform which contains the attributes of the factorization for any composite number utilizing complex variable factorization.

Plot Of the Infinite Product of the Product Representation for Sin(pi*x/n) in the 3-D Complex Plane:

Plot Of the Infinite Product of the Product Representation for Sin(pi*x/n) in the 2-D Complex Plane:

Plot Of the Normalized Infinite Product of the Product Representation for Sin(pi*x/n) in the 3-D Complex Plane:

Plot Of the Normalized Infinite Product of Sin(pi*x/n) in the 3-D Complex Plane:

Plot Of the Cos of the Infinite Product of the product representation of Sin(pi*x/n) in the 3-D Complex Plane:

If you want to learn more about the Riemann Hypothesis and the Millenium prize problems you can find them at the following sources:

Riemann Hypothesis:

https://mathworld.wolfram.com/RiemannZetaFunction.html

https://mathworld.wolfram.com/RiemannZetaFunctionZeros.html

https://en.wikipedia.org/wiki/Particular_values_of_the_Riemann_zeta_function

Clay Maths Institute's Millenium Prize Problems:

https://en.wikipedia.org/wiki/Millennium_Prize_Problems

Musical Representation for the Sieve of Eratosthenes:

https://www.youtube.com/watch?v=Ofg8fG-1iJA

https://www.youtube.com/watch?v=zhNnmtnV2cU

Also Here are some relevant sources for the project:

http://www-elsa.physik.uni-bonn.de/~dieckman/InfProd/InfProd.html

https://ocw.mit.edu/courses/18-104-seminar-in-analysis-applications-to-number-theory-fall-2006/58778de0faae6448c3b0bfb1a1ec4f7a_chan.pdf

https://www.jstor.org/stable/3615085

https://osf.io/4afqj/download

https://www.parabola.unsw.edu.au/files/articles/2020-2029/volume-57-2021/issue-2/vol57_no2_3.pdf

https://www.maa.org/sites/default/files/pdf/pubs/monthly_augsep12_page645.pdf

https://mathworld.wolfram.com/DedekindEtaFunction.html

https://mathworld.wolfram.com/InfiniteProduct.html

https://mathworld.wolfram.com/PolygonCircumscribing.html

https://math.stackexchange.com/questions/186292/derivatives-of-the-riemann-zeta-function-at-s-0

https://www.youtube.com/watch?v=BuKgxeer9j8

https://www2.karlin.mff.cuni.cz/~slavik/product/product_integration.pdf

https://mathstats.uncg.edu/number-theory/wp-content/uploads/sites/6/2018/01/zvengrowski-converge-eulerprod.pdf

https://www.youtube.com/watch?v=cjKtzzACyhI

https://www.youtube.com/watch?v=bo798KEKoDI

https://www.youtube.com/watch?v=fpqGRVtBER4

https://www.youtube.com/watch?v=8x374slJGuo&t=61s

https://www.youtube.com/watch?v=jnxqHcObNK4

https://www.youtube.com/watch?v=0kXGb0_-1iY

https://unsolvedproblems.org/S132.pdf

About Me

My name is Leo Borcherding, I am a Software Developer with experience working on programs for encryption of firmware devices. I have a background in electrical engineering and my passion is mathematics as well as art. I am developing this software so that we can further our understanding of mathematics, physics, and the universe. Please contact me at borchborchmail@gmail.com if you have questions or are able to do something interesting with my software or math. You can also leave feedback on the software in this submission form:

https://docs.google.com/forms/d/e/1FAIpQLSedobin-e8XqIv2AgMWhIrcNq-Pm7fsD63rhjuEiksWMAe9Og/viewform?usp=sf_link

Here is an example of the current capabilities of Bing chat with GPT4:

Ultimately knowledge should be free however it takes a lot of time and work to develop the mathematics, proofs and software required, I would really appreciate it, if you feel inclined to donate to help me keep developing this software and writing this paper. You can find the donation link in the file called bitcoin_donation_wallet.txt

Also if you want read my original paper I wrote in 2020 which initially started my journey on the Riemann Hypothesis here:

https://docs.google.com/document/d/1EqDpk-XiKePku2qzsUmaPO4Ejpdq4HKg/edit

and want to see my previous work on tetrahedral families from 2017 you can find that here:

https://oeis.org/A287324

https://oeis.org/A287324/a287324_2.pdf