Algorithmic Complexity Bounds for the De Bruijn-Newman Constant and Efficient Verification of the Riemann Hypothesis

Abstract

This paper establishes rigorous algorithmic complexity bounds for verifying the Riemann Hypothesis (RH) through the de Bruijn-Newman constant Λ.

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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