Advances in Ramanujan Partition Theory and Rogers-Ramanujan Identities — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: The user wants me to analyze the provided research findings about Ramanujan's partition function and related topics. Let me extract the key mathematical insights from these findings. The findings mention: 1. Rogers-Ramanujan Identities proof by Andrews and Baxter 2. Asymptotics of restricted partition functions by Ayla Gafni 3. Integer partitions webinar by Prof. Kalyan Chakraborty 4. Rogers-Ramanujan identities part 2 (German) 5. Partition function/Zustandssumme lecture 6. Ramanujan's unpublished manuscript on partition and tau functions (arXiv:math/0201265v2) Key mathematical content: - Rogers-Ramanujan identities: Two famous identities relating infinite products to infinite series - Partition function p(n) and restricted partition functions p_A(n) - Tau function τ(n) (Ramanujan's tau function) - Congruences for partition function and tau function - Asymptotics of partition functions The Rogers-Ramanujan identities are: G(q) = Σ_{n=0}^∞ q^{n²} / (q;q)_n = 1 / (q;q^5)_∞ (q^4;q^5)_∞ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225574059