Cyclotomic Polynomials at Non-Primitive Roots via Möbius Inversion — E8 Intelligence Research

FINDING: Fourier evaluation of cyclotomic polynomials at non-primitive roots of unity yields explicit closed forms via Möbius inversion, linking discrete harmonic analysis to root-system structure. | MATH: For Φₙ(x) (minimal polynomial of primitive n-th roots), at a k-th root ζ (k|n, k 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
2026-09-25
DOI
https://doi.org/10.5281/zenodo.22951621
Primary Topic
Polynomial and algebraic computation
Type
preprint
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preprint

Cyclotomic Polynomials at Non-Primitive Roots via Möbius Inversion — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Polynomial and algebraic computation
preprint

Cyclotomic Polynomials at Non-Primitive Roots via Möbius Inversion — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Fourier evaluation of cyclotomic polynomials at non-primitive roots of unity yields explicit closed forms via Möbius inversion, linking discrete harmonic analysis to root-system structure. | MATH: For Φₙ(x) (minimal polynomial of primitive n-th roots), at a k-th root ζ (k|n, k Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Polynomial and algebraic computation
DOIOpen Access PDFOpenAlex
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Cyclotomic Polynomials at Non-Primitive Roots via Möbius Inversion — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS