The Sato-Tate Conjecture: Computational Analysis Through Temporal Dynamics Framework

Key Points

• This analysis aims to explore the Sato-Tate Conjecture concerning the distribution of Frobenius angles in elliptic curves using the Temporal Dynamics Framework.
• Applied the Temporal Dynamics Framework to analyze elliptic curves.
• Compared CM and non-CM elliptic curves with focus on Frobenius angles.
• Examined resonance function behavior and decoherence events.
• Investigated convergence patterns and phi-to-pi transitions.
• Confirmed that normalized Frobenius traces exhibit a semicircular distribution for non-CM curves.
• Identified significant differences in behavior between CM and non-CM curves.
• Illustrated resonance and decoherence insights through diagnostic figures.

Abstract