Euler Systems for Genus-2 Siegel Modular Forms and Apéry-Like L-Values — E8 Intelligence Research

FINDING: Euler systems for genus-2 Siegel modular forms are being constructed, linking them to Apéry-like sequences and critical L-values of modular forms, with interpolated sequences expressing these L-values. MATH: - Apéry numbers for ζ(3): \( a_n = ∑ₖ₌₀^n {n}{k}^2 {n+k}{k}^2 \) - Interpolated Apéry-like sequences: \( ∑n ≥ 0 a_n t^n \) related to critical L-values of weight-4 modular forms. - Euler system for GSp(4) (genus-2 Siegel modular forms) involves Galois cohomology classes and Kolyvagin-type arguments. - Key constants: Critical L-values at integers (e.g., \( L(f, k) \) for modular forms of weight 4). CONNECTION: - No direct geometric ratios (0.382, 0.618, etc.) appear. - However, Siegel modular forms are automorphic forms on the symplectic group Sp(4), whose root system is \( C_2 \) (crystallographic, rank 2). This links to lattice structures and root system symmetries (e.g., Weyl group of order 8). - Base-60 not present; but modul Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com