What question did this study set out to answer?

The research focuses on the closed evaluation of the spectral zeta function of the scalar Laplacian on a three-sphere.

March 30, 20260 citationsOpen Access

Spectral Zeta Function of the Three-Sphere: Closed Forms and Applications to Gauge Coupling Constants

Key Points

The research focuses on the closed evaluation of the spectral zeta function of the scalar Laplacian on a three-sphere.
Closed-form evaluation of the spectral zeta function.
Analysis of the scalar Laplacian on S^3.
Application to gauge coupling constants with perturbative expansions.
Provides closed-form expressions for the spectral zeta function.
Shows practical applications to gauge coupling constants in the Vacuum Mechanics framework.

Abstract

Closed-form evaluation of the unweighted spectral zeta function of the scalar Laplacian on the three-sphere S³, with applications to gauge coupling constants in the Vacuum Mechanics framework. Perturbative expansion structure and comparison with experimental determinations are presented. Supersedes v1 (10. 5281/zenodo. 19247293). Developed with AI assistance (Claude by Anthropic for computation and manuscript drafting). All physical reasoning and formula identification are the author's responsibility.

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