Work

Proofs of Mizuno’s conjectures on generalized rank two Nahm sums

Year: 2025

Type: article

Abstract: Recently, Mizuno studied generalized Nahm sums associated with symmetrizable matrices. He provided 14 sets of candidates of modular Nahm sums in rank two and justified four of them. We prove the modularity for eight other sets of candidates and present conjectural formulas for the remaining two sets of candidates. This is achieved by finding Rogers–Ramanujan type identities associated with these Nahm sums. We also prove Mizuno’s conjectural modular transformation formula for a vector-valued function consisting of Nahm sums. Meanwhile, we find some new non-modular identities for some other Nahm sums associated with the matrices in Mizuno’s candidates.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/9496

Authors: Boxue Wang, Liuquan Wang

Institution: Wuhan University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G4065328272