Zagier's Sporadic Sequences Interpolate Critical L-Values of Weight-4 Modular Forms — E8 Intelligence Research

FINDING: Zagier's sporadic sequences (Apéry-like) interpolate to critical L-values of weight-4 modular forms, extending the ζ(3) Apéry number connection. | MATH: Interpolated Apéry numbers for ζ(3) → critical L-value of weight-4 modular form. Generalization: six sporadic sequences (Zagier's list) yield critical L-values of weight-4 modular forms. Key constants: critical L-values at s = (weight)/2 = 2 for weight-4 forms. No explicit ratios (0.382, 0.618, etc.) appear in the abstract or titles. | CONNECTION: No direct geometric harmony ratios or base-60 or crystallographic symmetries are mentioned. However, weight-4 modular forms are linked to Eisenstein series of weight 4, which have Fourier coefficients related to divisor sums (σ₃(n)), and these appear in lattice theta series for the root lattice D₄ or E₈ (crystallographic). The critical L-value interpolation may involve periods of modular forms, which are related to volumes of hyperbolic 3-manifolds or Shimura curves, but this is not Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com