Spectral Zeta Functions of Modular Quantum Networks and the Riemann Hypothesis

Abstract

We investigate a novel class of spectral zeta functions arising from modular quantum networks, establishing a rigorous correspondence between the non-trivial zeros of the Riemann zeta function and the resonances of an adelic quantum network $\mathcal{Q}_\mathbb{A}$.

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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