What question did this study set out to answer?

To examine the analytical connections between the Rogers-Ramanujan identities, Ramanujan partition congruences, and modular forms.

August 19, 2026Open Access

Rogers-Ramanujan Identities: Partition Congruences and Modular Form Connections — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Mathematical analysis reveals structural links between partition congruences and modular forms, highlighting algebraic symmetries tied to the golden ratio.

Key Points

To examine the analytical connections between the Rogers-Ramanujan identities, Ramanujan partition congruences, and modular forms.
Analyzed q-series expansions of the Rogers-Ramanujan identities in relation to the partition function p(n).
Evaluated arithmetic congruence relations for Ramanujan's tau function τ(n) modulo small prime numbers.
Characterized fundamental partition congruences including p(5k+4) ≡ 0 (mod 5), p(7k+5) ≡ 0 (mod 7), and p(11k+6) ≡ 0 (mod 11).
Demonstrated algebraic connections between modulus 5 q-series generating functions, the golden ratio φ ≈ 1.618, and affine root systems.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a858aaf03308d306e2d8040 https://doi.org/10.5281/zenodo.21973594

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Implication

Mathematical analysis reveals structural links between partition congruences and modular forms, highlighting algebraic symmetries tied to the golden ratio.

Rogers-Ramanujan Identities: Partition Congruences and Modular Form Connections — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

Rogers-Ramanujan Identities: Partition Congruences and Modular Form Connections — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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