Anisotropic Deformations of the Riemann Xi-Function and Zero Dynamics on the Critical Line

Abstract

We investigate a family of anisotropic deformations $\xi_{t,\alpha}(s)$ of the Riemann xi-function, originally introduced in the context of spectral determinants by the authors of arXiv:2601.15966v1.

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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