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This work aims to construct a geometric equivalent of the Riemann zeta function and explore its implications for open problems in number theory.

May 22, 2026Open Access

An Equivalent Geometric Construction of the ζ Function: From Euler Nested Circles to Sphere Helix

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Randomized trial establishes a geometric equivalent of the Riemann ζ function, indicating new insights in number theory.

This work aims to construct a geometric equivalent of the Riemann zeta function and explore its implications for open problems in number theory.
Constructed geometrically from Euler series with symmetry conditions.
Verified algebraic identities and geometrical properties numerically.
Derived results related to magnetic fields and Goldbach modulus distribution formulas.
Establishes a rigorous identity ζ(s) = (2^s − 1)^(−1) Σ 1/r_n^s for Re(s) > 1, verified to machine precision.
Derived the Goldbach modulus distribution P(m > 2 - ε) = tanh(√ε) verified from Goldbach decompositions.
Characterized zero locations of ζ function in the critical strip using geometric properties.

Lixin Wang (2026) studied this question.

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