This analysis demonstrates the connection between the fine structure constant and Riemann zeta function zeros, indicating a bridge between number theory and physics.
We demonstrate that the fine structure constant alpha⁻¹ ≈ 137.036 emerges necessarily from the deepest mathematical structure of reality: the zeros of the Riemann zeta function zeta(s). We present an exact formula connecting alpha⁻¹ to the first four nontrivial zeros gamma_1, gamma_2, gamma_3, gamma_4 of zeta(1/2 + it). The derivation combines spectral theory of magnetic Schrodinger operators on hyperbolic surfaces, the Selberg-Gutzwiller trace formula, and arithmetic geometry. The resulting value matches the experimental CODATA 2018 value with precision 2.1 × 10⁻¹⁰. This establishes a profound connection between number theory and fundamental physics.
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Felipe Oliveira Souto (2025) studied this question.
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