Liuquan Wang

activity

20222026

collaborators

17 papers

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…

math.CO2025

Nahm sum identities for Cartan matrices of type $D_{k}$

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 $D_{k}$ . Three of these had been conjectured by Flohr,…

math.NT2025

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…

math.NT2025

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…

math.NT2025

Modularity of tadpole Nahm sums in ranks 4 and 5

Changsong Shi, Liuquan Wang

Around 2016, Calinescu, Milas and Penn conjectured that the rank $r$ Nahm sum associated with the $r \times r$ tadpole Cartan matrix is modular, and they provided a proof for $r = 2$ .…

math.NT2025

Rogers--Ramanujan Type Identities for Rank Two Partial Nahm Sums

Liuquan Wang, Wentao Zeng

Let $A$ be a $r \times r$ rational nonzero symmetric matrix, $B$ a rational column vector, $C$ a rational scalar. For any integer lattice $L$ and vector $v$ of $Z^{r}$ , we de…

math.NT2024

Modularity of Some Nahm Sums as Vector-valued Functions

Liuquan Wang, Huohong Zhang

Zagier observed that modular Nahm sums associated with the same matrix may form a vector-valued modular function on some congruence subgroup. We establish modular transformation fo…

math.NT2024

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…

math.NT2024

Counterexamples to Zagier's Duality Conjecture on Nahm Sums

Liuquan Wang

Given any positive integer $r$ , Nahm's problem is to determine all $r \times r$ rational positive definite matrix $A$ , $r$ -dimensional rational vector $B$ and rational scalar $C$ su…

math.NT2024

Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index $(1, 2, 2)$

Boxue Wang, Liuquan Wang

Mizuno provided 15 examples of generalized rank three Nahm sums with symmetrizer $diag (1, 2, 2)$ which are conjecturally modular. Using the theory of Bailey pairs and some $…

math.NT2024

Mizuno's rank three Nahm sums I: identities of index $(1, 1, 2)$

Boxue Wang, Liuquan Wang

Mizuno provided 19 examples of generalized rank three Nahm sums with symmetrizer $diag (1, 1, 2)$ which are conjecturally modular. We confirm their modularity by establishing…

math.NT2024

Leading coefficient in the Hankel determinants related to binomial and $q$ -binomial transforms

Shane Chern, Lin Jiu, Shuhan Li +1

It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to…

math.NT2022

Identities on Zagier's rank two examples for Nahm's problem

Liuquan Wang

Let $r \geq 1$ be a positive integer, $A$ a real positive definite symmetric $r \times r$ matrix, $B$ a vector of length $r$ , and $C$ a scalar. Nahm's problem is to describe all such…

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

Nahm sum identities for Cartan matrices of type Dk​

Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples

Proofs of Two Conjectural Identities on Partial Nahm Sums

Modularity of tadpole Nahm sums in ranks 4 and 5

Rogers--Ramanujan Type Identities for Rank Two Partial Nahm Sums

Modularity of Some Nahm Sums as Vector-valued Functions

Some New Modular Rank Three Nahm Sums from a Lift-Dual Operation

Counterexamples to Zagier's Duality Conjecture on Nahm Sums

Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index (1,2,2)

Mizuno's rank three Nahm sums I: identities of index (1,1,2)

Leading coefficient in the Hankel determinants related to binomial and q-binomial transforms

Identities on Zagier's rank two examples for Nahm's problem

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 $D_{r}$

Nahm sum identities for Cartan matrices of type $D_{k}$

Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index $(1, 2, 2)$

Mizuno's rank three Nahm sums I: identities of index $(1, 1, 2)$

Leading coefficient in the Hankel determinants related to binomial and $q$ -binomial transforms