5 papers
Some new modular Nahm sums of ranks 3 and 4
Zhineng Cao, Liuquan Wang
We discover six new families of modular Nahm sums in ranks 3 and 4. Two of them are rank three sums obtained by modifying two of Zagier's rank three examples. Three rank four famil…
Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples
Zhineng Cao, Liuquan Wang
We find nine new sets of rank four Nahm sums associated with nine different numeric matrices which are likely to be modular. They are discovered by applying the lift-dual operation…
Some New Modular Rank Three Nahm Sums from a Lift-Dual Operation
Zhineng Cao, Liuquan Wang
Around 2007, Zagier discovered some rank two and rank three Nahm sums, and their modularity have now all been confirmed. Zagier also observed that the dual of a modular Nahm sum is…
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…
Multi-sum Rogers-Ramanujan Type Identities
Zhineng Cao, Liuquan Wang
We use an integral method to establish a number of Rogers-Ramanujan type identities involving double and triple sums. The key step for proving such identities is to find some infin…