Liuquan Wang

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20222026

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math.CO2026

Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2 ℓ - 1}^{(2)}$

Liuquan Wang

We prove four conjectures of Takigiku and Tsuchioka consisting of eight Rogers--Ramanujan type identities. Two conjectures involve triple sums and a third involves quadruple sums,…

math.CO2026

Proofs of Some Kanade--Russell Mod 12 Conjectures

Liuquan Wang

Kanade and Russell conjectured seventeen Rogers--Ramanujan type identities of modulus 12. Eleven of these identities involving triple sums were proved by Bringmann--Jennings-Shaffe…

math.NT2026

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…

math.NT2026

Modular Nahm Sums for the Inverse Cartan Matrix of Type $D_{r}$

Liuquan Wang, Shangwen Wang

For $r \geq 3$ we denote by $C (D_{r})$ the Cartan matrix of type $D_{r}$ . Recently, Sun and Wang conjectured a Rogers--Ramanujan type identity for the Nahm sum associated with…

math.NT2026

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…

Proofs of four Takigiku--Tsuchioka conjectures on level 2 principal characters of A2ℓ−1(2)​

Proofs of Some Kanade--Russell Mod 12 Conjectures

Nahm Sums Dual to Zagier's Rank-Three Examples and Related Identities

Modular Nahm Sums for the Inverse Cartan Matrix of Type Dr​

Some new modular Nahm sums of ranks 3 and 4

Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2 ℓ - 1}^{(2)}$

Modular Nahm Sums for the Inverse Cartan Matrix of Type $D_{r}$