Partition Identities for Ramanujan's Third Order Mock Theta Functions

2010/06/16 by William Y. C. Chen, Chen, William Y. C., Kathy Q. Ji +3
Mathematics · #05A17 #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1006.3194

openalex publication_date 2010/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions ϕ(-q) and ψ(-q). We also give an involution for Fine's partition identity on the mock theta function f(q). The two classical identities of Ramanujan on third order mock theta functions are consequences of these partition identities. Our combinatorial constructions also apply to Andrews' generalizations of Ramanujan's identities.

Citations

• The Final Problem : An Account of the Mock Theta Functions

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