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The research aims to establish a geometric and dynamical foundation for the Riemann Hypothesis related to non-trivial zeros of the zeta function.

March 13, 2026Open Access

Equilibrium on the Riemann Sphere: Toward a Geometric Foundation for the Riemann Hypothesis

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The research aims to establish a geometric and dynamical foundation for the Riemann Hypothesis related to non-trivial zeros of the zeta function.
Developed a framework using stereographic embedding of Dirichlet partial sums into the Riemann sphere.
Utilized a second σ-derivative criterion to identify zeros as stable points in spherical geometry.
Presented three characterizations of σ = 1/2 using algebraic derivations and kinetic energy identities.
Validated that the second derivative condition ∂²Z_n/∂σ²|{σ=1/2} ≥ 0 suggests stability for the zeros.
Demonstrated log-log growth in phase-space volume V(σ, x) uniquely at σ = 1/2.
Confirmed analytic structures through numerical experiments on the first twenty non-trivial zeros.

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Analytic framework explores non-trivial zeros of the Riemann zeta function, suggesting geometric insights into its behavior.

Jeong Min Yeon (2026) studied this question.

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