What question did this study set out to answer?

This work aims to explore the connections between Rogers-Ramanujan identities, modular forms, and the golden ratio.

July 27, 2026Open Access

Rogers-Ramanujan Identities: Partitions, Modular Forms, and the Golden Ratio — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Mathematical exploration reveals connections between integer partitions, modular forms, and the golden ratio, suggesting new insights into their interplay.

Key Points

This work aims to explore the connections between Rogers-Ramanujan identities, modular forms, and the golden ratio.
Examined the Rogers-Ramanujan identities using continued fractions and q-series.
Analyzed mathematical expressions related to integer partitions and modular forms.
Explored the special values of the continued fraction at specific points.
Identities illustrate a clear connection between integer partitions and the golden ratio.
The continued fraction evaluates to the reciprocal of the golden ratio at a defined point.
The modular form is identified as a level-1 weight-12 cusp form linked to the identities.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a670c2a40bca442e0d4aee1 https://doi.org/10.5281/zenodo.21545326

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Implication

Mathematical exploration reveals connections between integer partitions, modular forms, and the golden ratio, suggesting new insights into their interplay.

Rogers-Ramanujan Identities: Partitions, Modular Forms, and the Golden Ratio — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

Rogers-Ramanujan Identities: Partitions, Modular Forms, and the Golden Ratio — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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