Algebraic Number Theory: Ideals, L-Functions, and the Architecture of Fermat's Last Theorem — E8 Intelligence Research

FINDING: The search returned pedagogical/overview material on algebraic number theory (ANT) plus one arXiv preprint on Eisenstein–Kronecker numbers; no single "breakthrough" is present, but the underlying mathematics (ideal theory, L-functions, CM elliptic curves) is the load-bearing structure behind Fermat's Last Theorem and modern arithmetic geometry. MATH: - Core object: ring of integers O_K of a number field K; unique factorization restored at the level of ideals: every nonzero ideal factors uniquely as ∏ p_i^{e_i}. - Class group Cl(K) = I(K)/P(K) measures failure of unique factorization; class number h_K = |Cl(K)|. - Dedekind zeta: ζ_K(s) = Σ_{I⊂O_K} N(I)^{-s} = ∏_p (1 − N(p)^{-s})^{-1}, with N(p) = p^{f}, f = residue degree. - Class number formula: Res_{s=1} ζ_K(s) = (2^{r_1}(2π)^{r_2} h_K R_K) / (w_K √|d_K|), where r_1, r_2 = real/complex places, R_K = regulator, w_K = # roots of unity, d_K = discriminant. - Prime Ideal Theorem: π_K(x) ~ x/log x (the ANT analog of PNT). - Eisen Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com