Euler Product, Cyclotomic Identities, and Divisor Sums: Prime Lattice Symmetries — E8 Intelligence Research

FINDING: Euler product formula for ζ(s) connects primes to analytic structure; cyclotomic polynomial identities and explicit divisor formulas reveal arithmetic lattice symmetries. MATH: - Euler product: ζ(s) = ∏_p (1 − p^{−s})^{-1}, valid for Re(s) > 1. - Cyclotomic identity: if a | b, then Φ_b(x) = Φ_a(x^{b/a}) / ∏_{d|a, d 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
2026-09-28
DOI
https://doi.org/10.5281/zenodo.23006859
Primary Topic
Analytic Number Theory Research
Type
preprint
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Euler Product, Cyclotomic Identities, and Divisor Sums: Prime Lattice Symmetries — E8 Intelligence Research

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

Euler Product, Cyclotomic Identities, and Divisor Sums: Prime Lattice Symmetries — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Euler product formula for ζ(s) connects primes to analytic structure; cyclotomic polynomial identities and explicit divisor formulas reveal arithmetic lattice symmetries. MATH: - Euler product: ζ(s) = ∏_p (1 − p^{−s})^{-1}, valid for Re(s) > 1. - Cyclotomic identity: if a | b, then Φ_b(x) = Φ_a(x^{b/a}) / ∏_{d|a, d Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Decent work and economic growth
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Euler Product, Cyclotomic Identities, and Divisor Sums: Prime Lattice Symmetries — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS