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Proofs of Mizuno's Conjectures on Generalized Rank Two Nahm Sums
Boxue Wang, Liuquan Wang
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…
Rogers-Ramanujan type identities involving double, triple and quadruple sums
Zhi Li, Liuquan Wang
We prove a number of new Rogers-Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of…
On Some Double Nahm Sums of Zagier
Zhineng Cao, Hjalmar Rosengren, Liuquan Wang
Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no -series pro…
Modularity of Nahm Sums for the Tadpole Diagram
Antun Milas, Liuquan Wang
We prove Rogers-Ramanujan type identities for the Nahm sums associated with the tadpole Cartan matrix of rank . These identities reveal the modularity of these sums, and thereby…