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): \ (aₙ = ₊=₀ⁿ nk² n+kk² \) - Interpolated Apéry-like sequences: \ (₍ ₀ aₙ tⁿ \) 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 \ (C₂ \) (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