Real Periods of Elliptic Curves Linked to Critical L-Values and Apéry Sequences — E8 Intelligence Research

July 21, 2026Open Access

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This research aims to explore the relationship between the real period of elliptic curves and the critical L-values of modular forms.
Evaluated the real period ω_E of elliptic curves using integrals over minimal Weierstrass models.
Utilized modularity to relate L(E,s) to modular forms of weight 2 on Γ₀(N).
Examined Apéry-like sequences and their connections to modular forms via interpolated numbers.
The ratio L(f,1)/Ω_E is rational, illustrating harmonic ratios in connection with elliptic curves.
Identified base-60 structures in periods of elliptic curves with complex multiplication (CM).
New connections between periods and L-values mirror the presence of the golden ratio in modular forms.

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Finding links real periods of elliptic curves to critical L-values of modular forms, suggesting new insights.

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Andrew Stewart Caldin (2026) studied this question.

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