Liuquan Wang

activity

20132026

most citedParity of coefficients of mock theta functions

12 citations · 48 across the 40 of their papers we have counts for

collaborators

40 papers

hep-th2026

Proofs of some conjectures of Okazaki and Smith on line defect half-indices of $SU (N)$ Chern-Simons theories

Liuquan Wang, Yiyang Yue

Okazaki and Smith discovered many elegant formulas expressing some matrix integrals as some celebrated $q$ -series such as the Rogers--Ramanujan functions or Jacobi theta functions.…

math.NT2023★ 1 cited

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…

math.CO2023

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…

math.NT2023

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 $q$ -series pro…

math.NT2023

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 $3$ . These identities reveal the modularity of these sums, and thereby…

math.NT2022

Explicit Forms and Proofs of Zagier's Rank Three Examples for Nahm's Problem

Liuquan Wang

Let $r \geq 1$ be a positive integer, $A$ a real positive semi-definite symmetric $r \times r$ rational matrix, $B$ a rational vector of length $r$ , and $C$ a rational scalar. Nahm's…

math.NT2022

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…

math.CO2022

New Proofs of Some Double Sum Rogers-Ramanujan Type Identities

Liuquan Wang

Recently, Rosengren utilized an integral method to prove a number of conjectural identities found by Kanade and Russell. Using this integral method, we give new proofs to some doub…

math.NT2021

Modular Proofs of Gosper's Identities

Liuquan Wang

We give unified modular proofs to all of Gosper's identities on the $q$ -constant $Π_{q}$ . We also confirm Gosper's observation that for any distinct positive integers $n_1,\cdots,n_m…

math.NT2021

Sign Changes of Coefficients of Powers of the Infinite Borwein Product

Liuquan Wang

We denote by $c_{t}^{(m)} (n)$ the coefficient of $q^{n}$ in the series expansion of $(q; q)_{\infty}^{m} (q^{t}; q^{t})_{\infty}^{- m}$ , which is the $m$ -th power of the infinite Borwein product. Le…

math.CO2021

Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product

Liuquan Wang

Andrews and Merca investigated a truncated version of Euler's pentagonal number theorem and showed that the coefficients of the truncated series are nonnegative. They also consider…

math.DG2021

Brouwer degree for Kazdan-Warner equations on a connected finite graph

Linlin Sun, Liuquan Wang

We study Kazdan-Warner equations on a connected finite graph via the method of the degree theory. Firstly, we prove that all solutions to the Kazdan-Warner equation with nonzero pr…

math.NT2021★ 2 cited

A Family of Supercongruences Involving Multiple Harmonic Sums

Megan McCoy, Kevin Thielen, Liuquan Wang +1

In recent years, the congruence $i + j + k = p i, j, k > 0 \sum \frac{1}{ij k} \equiv - 2 B_{p - 3} (mod p),$ first discovered by the last author have been generalized by eithe…

math.CO2020★ 3 cited

Positivity and divisibility of alternating descent polynomials

Zhicong Lin, Shi-Mei Ma, David G. L. Wang +1

The alternating descent statistic on permutations was introduced by Chebikin as a variant of the descent statistic. We show that the alternating descent polynomials on permutations…

math.NT2020

Modular units and cuspidal divisor classes on $X_{0} (n^{2} M)$ with $n ∣24$ and $M$ squarefree

Liuquan Wang, Yifan Yang

For a positive integer $N$ , let $C (N)$ be the subgroup of $J_{0} (N)$ generated by the equivalence classes of cuspidal divisors of degree $0$ and $\mathscr C(N)(\mathbb Q):=\…

math.NT2020★ 12 cited

Parity of coefficients of mock theta functions

Liuquan Wang

We study the parity of coefficients of classical mock theta functions. Suppose $g$ is a formal power series with integer coefficients, and let $c (g; n)$ be the coefficient of $q^{n}$ …

math.NT2020

Farey sequence and Graham's conjectures

Liuquan Wang

Let $F_{n}$ be the Farey sequence of order $n$ . For $S \subseteq F_{n}$ we let $Q (S) = {x / y : x, y \in S, x \leq y and y \neq = 0}$ . We show th…

math.NT2020

Ramanujan-type $1/ π$ -series from bimodular forms

Liuquan Wang, Yifan Yang

We develop an approach to establish $1/ π$ -series from bimodular forms. Utilizing this approach, we obtain new families of $2$ -variable $1/ π$ -series associated to Zagier's sporadic…

math.NT2019

Moments of ranks and cranks, and Quotients of Eisenstein Series and the Dedekind Eta Function

Liuquan Wang, Yifan Yang

Atkin and Garvan introduced the functions $N_{k} (n)$ and $M_{k} (n)$ , which denote the $k$ -th moments of ranks and cranks in the theory of partitions. Let $e_{2 r} (n)$ be the $n$ -th Four…

math.NT2018★ 1 cited

The smallest parts function associated with $ω (q)$

Liuquan Wang, Yifan Yang

We establish two families of congruences modulo powers of 5 for the Fourier coefficients of $(2 E_{2} (2 τ) - E_{2} (τ)) η (2 τ)^{- 1}$ , where $E_{2} (τ)$ is the weight 2 Eisenstein series and $η(τ…

math.NT2018

Representations of mock theta functions

Dandan Chen, Liuquan Wang

Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of pa…

math.CO2018

Some inequalities for Garvan's bicrank function of 2-colored partitions

Shane Chern, Dazhao Tang, Liuquan Wang

In order to provide a unified combinatorial interpretation of congruences modulo $5$ for 2-colored partition functions, Garvan introduced a bicrank statistic in terms of weighted v…

math.CO2018★ 1 cited

New Proofs of Ramanujan's Identities on False Theta Functions

Liuquan Wang

We provide new proofs to five of Ramanujan's intriguing identities on false theta functions without using the Rogers-Fine identity and Bailey transforms.

math.CO2018

Congruences Modulo Powers of 3 for 3- and 9-Colored Generalized Frobenius Partitions

Liuquan Wang

Let $c ϕ_{k} (n)$ be the number of $k$ -colored generalized Frobenius partitions of $n$ . We establish some infinite families of congruences for $c ϕ_{3} (n)$ and $c ϕ_{9} (n)$ modulo arbi…

Proofs of some conjectures of Okazaki and Smith on line defect half-indices of SU(N) Chern-Simons theories

Proofs of Mizuno's Conjectures on Generalized Rank Two Nahm Sums

Rogers-Ramanujan type identities involving double, triple and quadruple sums

On Some Double Nahm Sums of Zagier

Modularity of Nahm Sums for the Tadpole Diagram

Explicit Forms and Proofs of Zagier's Rank Three Examples for Nahm's Problem

Multi-sum Rogers-Ramanujan Type Identities

New Proofs of Some Double Sum Rogers-Ramanujan Type Identities

Modular Proofs of Gosper's Identities

Sign Changes of Coefficients of Powers of the Infinite Borwein Product

Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product

Brouwer degree for Kazdan-Warner equations on a connected finite graph

A Family of Supercongruences Involving Multiple Harmonic Sums

Positivity and divisibility of alternating descent polynomials

Modular units and cuspidal divisor classes on X0​(n2M) with n∣24 and M squarefree

Parity of coefficients of mock theta functions

Farey sequence and Graham's conjectures

Ramanujan-type 1/π-series from bimodular forms

Moments of ranks and cranks, and Quotients of Eisenstein Series and the Dedekind Eta Function

The smallest parts function associated with ω(q)

Representations of mock theta functions

Some inequalities for Garvan's bicrank function of 2-colored partitions

New Proofs of Ramanujan's Identities on False Theta Functions

Congruences Modulo Powers of 3 for 3- and 9-Colored Generalized Frobenius Partitions

Proofs of some conjectures of Okazaki and Smith on line defect half-indices of $SU (N)$ Chern-Simons theories

Modular units and cuspidal divisor classes on $X_{0} (n^{2} M)$ with $n ∣24$ and $M$ squarefree

Ramanujan-type $1/ π$ -series from bimodular forms

The smallest parts function associated with $ω (q)$