12 papers
Nahm Sums Dual to Zagier's Rank-Three Examples and Related Identities
Changsong Shi, Liuquan Wang
In 2007, Zagier identified twelve families of candidates for rank-three modular Nahm sums and established the modularity of three of them. The remaining cases were subsequently con…
Modular Nahm Sums for the Inverse Cartan Matrix of Type
Liuquan Wang, Shangwen Wang
For we denote by the Cartan matrix of type . Recently, Sun and Wang conjectured a Rogers--Ramanujan type identity for the Nahm sum associated with…
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…
Nahm sum identities for Cartan matrices of type
Liuquan Wang, Shangwen Wang
Around 2007, Warnaar proved four identities related to Nahm sums associated with twice the inverse of the Cartan matrix of type . Three of these had been conjectured by Flohr,…
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…
Proofs of Two Conjectural Identities on Partial Nahm Sums
Changsong Shi, Liuquan Wang
Recently, Wang and Zeng investigated modularity of partial Nahm sums and discovered 14 modular families of such sums. They confirmed modularity for 13 families and proposed a conje…