Rogers-Ramanujan Continued Fraction: Linking Modular Forms, Golden Ratio, and Quintic Solvability — E8 Intelligence Research

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The Rogers-Ramanujan continued fraction is deeply linked to the Dedekind eta function, modular transformations, and the golden ratio, and provides an algebraic solution to the general quintic equation. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.21617142

July 27, 2026Open Access

Rogers-Ramanujan Continued Fraction: Linking Modular Forms, Golden Ratio, and Quintic Solvability — E8 Intelligence Research

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Key Points

To explore the connections between the Rogers-Ramanujan continued fraction, modular forms, and their role in solving quintic equations.
Analyzed the Rogers-Ramanujan continued fraction (RRCF) and its relation to the Dedekind eta function and modular transformations.
Calculated specific values of RRCF using formulae for different values of q.
Established a link between RRCF and golden ratio as well as algebraic solutions to quintic equations.
RRCF provides an algebraic solution for the general quintic equation, linking to the Dedekind eta function and modular transformations.
Specific values of the continued fraction at certain q demonstrate proximity to the golden ratio, reinforcing their mathematical significance in quintic resolution.

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Implication

This research demonstrates the algebraic relationship between the Rogers-Ramanujan continued fraction and the golden ratio in solving quintic equations.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a69a2a3c8da07d9defa6436 https://doi.org/10.5281/zenodo.21617142

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Rogers-Ramanujan Continued Fraction: Linking Modular Forms, Golden Ratio, and Quintic Solvability — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Rogers-Ramanujan Continued Fraction: Linking Modular Forms, Golden Ratio, and Quintic Solvability — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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