Pedagogical Exposition of the Dedekind Zeta Function and Analytic Class Number Formula — E8 Intelligence Research

FINDING: The search returned pedagogical/expository material on the Dedekind zeta function and the analytic class number formula, not new computational results. | MATH: The analytic class number formula for a number field K: Res_{s=1} ζ_K(s) = (2^{r₁} (2π)^{r₂} h_K R_K) / (w_K √|d_K|), where r₁ = real embeddings, r₂ = complex pairs, h_K = class number, R_K = regulator, w_K = roots of unity, d_K = discriminant. Functional equation: ζ_K(s) = ζ_K(1−s) · |d_K|^{s−1/2} · [Γ(s/2)^{r₁} Γ(s)^{r₂} · 2^{r₁} · π^{r₂·s} / (2^{r₂} π^{r₁/2·... })] (conductor-discriminant form). | CONNECTION: No direct geometric-harmony constants (0.618, 1.618, base-60, root systems) appear in the retrieved sources. The regulator R_K is a covolume of the unit lattice in log-space — a lattice structure, but no φ-ratio or crystallographic symmetry is invoked. | DEPTH: 2 — Sources are introductory videos and a Wikipedia survey reference; no explicit computation, no new constants, no geometric-harmony link. The class num Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23756068
Primary Topic
Analytic Number Theory Research
Type
preprint
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Pedagogical Exposition of the Dedekind Zeta Function and Analytic Class Number Formula — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Pedagogical Exposition of the Dedekind Zeta Function and Analytic Class Number Formula — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The search returned pedagogical/expository material on the Dedekind zeta function and the analytic class number formula, not new computational results. | MATH: The analytic class number formula for a number field K: Res_{s=1} ζ_K(s) = (2^{r₁} (2π)^{r₂} h_K R_K) / (w_K √|d_K|), where r₁ = real embeddings, r₂ = complex pairs, h_K = class number, R_K = regulator, w_K = roots of unity, d_K = discriminant. Functional equation: ζ_K(s) = ζ_K(1−s) · |d_K|^{s−1/2} · [Γ(s/2)^{r₁} Γ(s)^{r₂} · 2^{r₁} · π^{r₂·s} / (2^{r₂} π^{r₁/2·... })] (conductor-discriminant form). | CONNECTION: No direct geometric-harmony constants (0.618, 1.618, base-60, root systems) appear in the retrieved sources. The regulator R_K is a covolume of the unit lattice in log-space — a lattice structure, but no φ-ratio or crystallographic symmetry is invoked. | DEPTH: 2 — Sources are introductory videos and a Wikipedia survey reference; no explicit computation, no new constants, no geometric-harmony link. The class num Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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Pedagogical Exposition of the Dedekind Zeta Function and Analytic Class Number Formula — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS