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A Rigorous Spectral and Modular Proof of the Riemann Hypothesis

Year: 2025

Type: article

Abstract: The Riemann Hypothesis states that all nontrivial zeros of the Riemann zeta function ζ(s) lie on the critical line ℜ(s) = 1/2. This paper presents a rigorous proof leveraging spectral rigidity and modular transformations. We show that any deviation from the critical line induces spectral instability in the Laplacian eigenvalues and disrupts modular symmetry, leading to a contradiction. Thus, all nontrivial zeros must satisfy ℜ(s) = 1/2

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15051242

Author: Musembi, Joshua Mwendwa

Institution: Jomo Kenyatta University of Agriculture and Technology

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6911812941

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