Mizuno's rank three Nahm sums I: identities of index (1,1,2)

2024/02/09 by Boxue Wang, Wang, Boxue, Liuquan Wang +1
Computer Science · Mathematics · #11F03 #11P84 #33D15 #33D60 #Advanced Mathematical Identities #Advanced Mathematical Theories #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2402.06253

openalex publication_date 2024/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mizuno provided 19 examples of generalized rank three Nahm sums with symmetrizer diag(1,1,2) which are conjecturally modular. We confirm their modularity by establishing Rogers--Ramanujan type identities of index (1,1,2) for these examples. We first reduce these Nahm sums to some double sums or single sums, and then we use known results or apply the theory of Bailey pairs to prove the desired identities. Meanwhile, we generalize some triple sum identities to general multi-sum identities.

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