Helen W. J. Zhang

collaborators

6 papers

math.NT2022

Congruences for modular forms and applications to crank functions

Hao Zhang, Helen W. J. Zhang

In this paper, motivated by the work of Mahlburg, we find congruences for a large class of modular forms. Moreover, we generalize the generating function of the Andrews-Garvan-Dyso…

math.NT2022

Higher order log-concavity of the overpartition function and its consequences

Gargi Mukherjee, Helen W. J. Zhang, Ying Zhong

Let $p ˉ (n)$ denote the overpartition function. In this paper, we study the asymptotic higher order $lo g$ -concavity property of the overpatition function in a similar framewor…

math.CO2018

The Unimodality of the Crank on Overpartitions

Wenston J. T. Zang, Helen W. J. Zhang

Let $N (m, n)$ denote the number of partitions of $n$ with rank $m$ , and let $M (m, n)$ denote the number of partitions of $n$ with crank $m$ . Chan and Mao proved that for any nonnegat…

math.CO2018

Inequalities for the overpartition function

Edward Y. S. Liu, Helen W. J. Zhang

Let $p (n)$ denote the overpartition funtion. Engel showed that for $n \geq 2$ , $p (n)$ satisfied the Turán inequalities, that is, $\overline{p}(n)^2-\overline{p}…

math.CO2018

$M_{2}$ -Ranks of overpartitions modulo $6$ and $10$

Helen W. J. Zhang

In this paper, we obtain inequalities on $M_{2}$ -ranks of overpartitions modulo $6$ . Let $N_{2} (s, m, n)$ to be the number of overpartitions of $n$ whose $M_{2}$ -rank is congrue…

math.CO2018

Generalized Lambert Series Identities and Applications in Rank Differences

Bin Wei, Helen W. J. Zhang

In this article, we prove two identities of generalized Lambert series. By introducing what we call $S$ -series, we establish relationships between multiple generalized La…

Congruences for modular forms and applications to crank functions

Higher order log-concavity of the overpartition function and its consequences

The Unimodality of the Crank on Overpartitions

Inequalities for the overpartition function

M2​-Ranks of overpartitions modulo 6 and 10

Generalized Lambert Series Identities and Applications in Rank Differences

$M_{2}$ -Ranks of overpartitions modulo $6$ and $10$