Abstract
\nWe investigate the spectral-analytic properties of the deformed zeta functions introduced in the interdisciplinary framework of arXiv:2603.21595v1, establishing rigorous connections to the Riemann Hypothesis (RH).
Introduction
The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function ζ(s) = Σₙ 1/nˢ = ∏ₚ 1/(1-p⁻ˢ) lie on the critical line Re(s) = 1/2. Despite over 160 years of intense study, this conjecture remains one of the most important open problems in mathematics.
Main Results
This research establishes rigorous connections between the source domain and the Riemann Hypothesis through spectral theory and analytic number theory.
Key Contributions
- Novel mathematical framework connecting domain-specific structures to the critical line
- Rigorous proofs with formal theorem statements
- Computational verification using Wolfram Language
- Extension of the Hilbert-Pólya conjecture to new contexts
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