Version 1
: Received: 9 May 2024 / Approved: 10 May 2024 / Online: 13 May 2024 (03:09:42 CEST)
How to cite:
Ivanko, S.; Farag, P. Proof of the Riemann Hypothesis and the Modified Collatz Conjecture Using the Sophy-Peter Mathematical Framework. Preprints2024, 2024050707. https://doi.org/10.20944/preprints202405.0707.v1
Ivanko, S.; Farag, P. Proof of the Riemann Hypothesis and the Modified Collatz Conjecture Using the Sophy-Peter Mathematical Framework. Preprints 2024, 2024050707. https://doi.org/10.20944/preprints202405.0707.v1
Ivanko, S.; Farag, P. Proof of the Riemann Hypothesis and the Modified Collatz Conjecture Using the Sophy-Peter Mathematical Framework. Preprints2024, 2024050707. https://doi.org/10.20944/preprints202405.0707.v1
APA Style
Ivanko, S., & Farag, P. (2024). Proof of the Riemann Hypothesis and the Modified Collatz Conjecture Using the Sophy-Peter Mathematical Framework. Preprints. https://doi.org/10.20944/preprints202405.0707.v1
Chicago/Turabian Style
Ivanko, S. and Peter Farag. 2024 "Proof of the Riemann Hypothesis and the Modified Collatz Conjecture Using the Sophy-Peter Mathematical Framework" Preprints. https://doi.org/10.20944/preprints202405.0707.v1
Abstract
In this article, we present solutions for one of the oldest mathematical problems, the Collatz Conjecture, and provide a proof for the Riemann Hypothesis, utilizing a new number theory based on newly discovered number properties, which will also be presented in this paper. This is made possible through the Sophy-Peter mathematical framework, built upon this new number theory. The Collatz Conjecture will be disproven, but as an alternative, the Oscillating Theorem will be introduced, with its correctness proven within this article. Furthermore, we present the general version of the Riemann zeta function, developed based on the new number theory. The correctness of this function is verified by comparing it with existing results of the zeta function. Using this approach and the Sophy-Peter framework, we have successfully proven the Riemann Hypothesis, long considered a millennium problem. Moreover, since the general zeta function is proven, this implies the correctness of the new number theory and the Sophy-Peter framework.
Keywords
Sophy-Peter Framework, New Number Theory, Modified Collatz Conjecture, Oscillating Theorem, General Zeta Function, Proof of the Riemann Hypothesis
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
