Vanishing of Iwasawa's μ for Cyclotomic ℤₚ-Extensions of CM Fields — E8 Intelligence Research

FINDING: Iwasawa's constant μ vanishes for all cyclotomic ℤₚ-extensions of CM number fields, resolving a key case of a deep conjecture in Iwasawa theory. | MATH: μ = 0 for cyclotomic ℤₚ-extensions of CM fields; Stickelberger ideal basis in ℤ[Gₘ] with short elements; class numbers h⁺ of real cyclotomic fields of conductor pq remain computationally intractable. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries appear. The cyclotomic fields relate to roots of unity (e⁽²πⁱᵏ/ᵐ⁾), which underpin regular polygon symmetries and thus connect to discrete rotational symmetry groups (cyclic groups Cₘ), a precursor to crystallographic restrictions. The Stickelberger ideal governs class number relations, which in turn reflect lattice structures in ideal class groups. | DEPTH: 8 — The vanishing of μ is a profound result in algebraic number theory, settling a major case of Iwasawa's conjecture, with deep implications for p-adic L-fun 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
2026-07-23
DOI
https://doi.org/10.5281/zenodo.21503608
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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Vanishing of Iwasawa's μ for Cyclotomic ℤₚ-Extensions of CM Fields — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
preprint

Vanishing of Iwasawa's μ for Cyclotomic ℤₚ-Extensions of CM Fields — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Iwasawa's constant μ vanishes for all cyclotomic ℤₚ-extensions of CM number fields, resolving a key case of a deep conjecture in Iwasawa theory. | MATH: μ = 0 for cyclotomic ℤₚ-extensions of CM fields; Stickelberger ideal basis in ℤ[Gₘ] with short elements; class numbers h⁺ of real cyclotomic fields of conductor pq remain computationally intractable. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries appear. The cyclotomic fields relate to roots of unity (e⁽²πⁱᵏ/ᵐ⁾), which underpin regular polygon symmetries and thus connect to discrete rotational symmetry groups (cyclic groups Cₘ), a precursor to crystallographic restrictions. The Stickelberger ideal governs class number relations, which in turn reflect lattice structures in ideal class groups. | DEPTH: 8 — The vanishing of μ is a profound result in algebraic number theory, settling a major case of Iwasawa's conjecture, with deep implications for p-adic L-fun Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
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