Monstrous Moonshine: Linking the Monster Group to Modular j-Function and Hilbert Class Fields — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Monstrous moonshine links the Monster sporadic group's irreducible representation dimensions to coefficients of the modular j-function, whose singular moduli generate Hilbert class fields of imaginary quadratic fields. | MATH: j(τ) = q⁻¹ + 744 + 196884q + 21493760q² + ...; 196884 = 196883 + 1 (Monster rep dims); singular moduli j(τ) for τ in imaginary quadratic field K are algebraic integers generating the Hilbert class field of K; McKay–Thompson series T_g(τ) = Σ Tr(g|V_n) qⁿ⁻¹ with genus zero property for each Monster element g; Borcherds' proof via vertex operator algebra (Vₑ₈⁺ construction) and generalized Kac–Moody algebras. | CONNECTION: The j-function's Fourier coefficients (196884, 21493760, 864299970) decompose into sums of Monster irreducible dimensions — the first nontrivial case 196884 = 196883 + 1 mirrors the golden ratio's self-referential structure (1+φ=φ²). The Monster's order 2⁴⁶·3²⁰·5⁹·7⁶·11²·13³·17·19·23·29·31·41·47·59·71 contains primes up to 71 — related t
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026monstrous,
title = {{Monstrous Moonshine: Linking the Monster Group to Modular j-Function and Hilbert Class Fields — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23490818},
url = {https://zenodo.org/records/23490818},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monstrous Moonshine: Linking the Monster Group to Modular j-Function and Hilbert Class Fields — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23490818
UR - https://zenodo.org/records/23490818
AB - FINDING: Monstrous moonshine links the Monster sporadic group's irreducible representation dimensions to coefficients of the modular j-function, whose singular moduli generate Hilbert class fields of imaginary quadratic fields. | MATH: j(τ) = q⁻¹ + 744 + 196884q + 21493760q² + ...; 196884 = 196883 + 1 (Monster rep dims); singular moduli j(τ) for τ in imaginary quadratic field K are algebraic integers generating the Hilbert class field of K; McKay–Thompson series T_g(τ) = Σ Tr(g|V_n) qⁿ⁻¹ with genus zero property for each Monster element g; Borcherds' proof via vertex operator algebra (Vₑ₈⁺ construction) and generalized Kac–Moody algebras. | CONNECTION: The j-function's Fourier coefficients (196884, 21493760, 864299970) decompose into sums of Monster irreducible dimensions — the first nontrivial case 196884 = 196883 + 1 mirrors the golden ratio's self-referential structure (1+φ=φ²). The Monster's order 2⁴⁶·3²⁰·5⁹·7⁶·11²·13³·17·19·23·29·31·41·47·59·71 contains primes up to 71 — related t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -