No Primary Research Found on Explicit Class Number Computations — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The search returned pedagogical/media content on the Dedekind zeta function and Riemann zeta function, not primary research on explicit class number computations. No new mathematical result is present in these sources. MATH: The relevant mathematical content these sources gesture toward is the **analytic class number formula** for a number field $K$: $$\lim_{s\to 1}(s-1)\,\zeta_K(s) = \frac{2^{r_1}(2\pi)^{r_2}\,h_K\,R_K}{w_K\sqrt{|d_K|}}$$ where: - $r_1$ = number of real embeddings, $r_2$ = number of conjugate pairs of complex embeddings, $n = r_1 + 2r_2 = [K:\mathbb{Q}]$ - $h_K$ = class number, $R_K$ = regulator (determinant of the log-embedding lattice) - $w_K$ = number of roots of unity in $K$ - $d_K$ = discriminant Euler factor: $\zeta_K(s) = \prod_{\mathfrak{p}} \left(1 - N(\mathfrak{p})^{-s}\right)^{-1}$ Functional equation: $\zeta_K(s) = |d_K|^{s-1/2}\left(\frac{\Gamma(s/2)}{\pi^{s/2}}\right)^{r_1}\left(\frac{\Gamma(s)}{(2\pi)^s}\right)^{r_2}\zeta_K(1-s)$ Regulato Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225266815
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