What question did this study set out to answer?

This research aims to establish a three-dimensional geometric representation of the Riemann ζ function.

June 4, 2026Open Access

An Equivalent Geometric Construction of the ζ Function: From Euler Nested Circles to Sphere Helix — Two Argument Paths (V12)

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Innovative geometric approach constructs a sphere helix representing the Riemann ζ function.

This research aims to establish a three-dimensional geometric representation of the Riemann ζ function.
Constructed a sphere helix from the series structure ζ(s) = Σ 1/nˢ with specific geometric requirements.
Developed two argument paths (Gaussian and Maxwell) that yield distinct geometric constructs.
Applied symmetry conditions to determine key geometric points and constructs.
Path A produces two orthogonal curve families with a common intersection at V = 1/2.
Path B fulfills the hairy ball theorem, confining closure to singularities at σ = 1/2.
The unique conditions result in a consistent geometric representation aligned with Riemann's hypotheses.

Lixin Wang (2026) studied this question.

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