Finding the proof of the Riemann hypothesis

Jonathan Jared Wilson
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Jonathan Jared Wilson: Purdue University

No yvq3p, OSF Preprints from Center for Open Science

Abstract: This paper presents steps proving the Riemann Hypothesis, one of the most significant unsolved problems in mathematics. By introducing the Gödel-Mandelbrot Duality Theorem and the Topological Tensor Factorization Theorem, they achieve a new framework for understanding the Riemann zeta function. Our method combines techniques from complex analysis, algebraic geometry, number theory, symplectic geometry[10], and representation theory to provide a comprehensive view of the zeta function's properties. Then demonstrate that the critical line Re(s) = 1/2 is a geometric invariant under the action of the symplectic group Sp(4,ℤ) and show how the zeta function can be factorized into a tensor product of simpler functions. This factorization allows us to analyze the distribution of zeros in each component, ultimately leading to a proof of the Riemann Hypothesis. The implications of this work extend beyond number theory, potentially impacting fields such as quantum physics, cryptography, and chaos theory.

Date: 2024-07-31
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:yvq3p

DOI: 10.31219/osf.io/yvq3p

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