N. Zhou

activity

20162026

most citedOn the distribution of rank and crank statistics for integer partitions

4 citations · 7 across the 23 of their papers we have counts for

collaborators

Showing 2018Show all

3 papers · 1 filter

math.NT2018

Proof of a conjecture of Farkas and Kra

Nian Hong Zhou

In this paper we prove a conjectured modular equation of Farkas and Kra, which involving a half sum of certain modular form of weight $1$ for congruence subgroup $Γ_{1} (k)$ with any…

math.NT2018

On the sum of the reciprocals of the differences between consecutive primes

Nian Hong Zhou

Let $p_{n}$ denote the $n$ -th prime number, and let $d_{n} = p_{n + 1} - p_{n}$ . Under the Hardy--Littlewood prime-pair conjecture, we prove \begin{align*} \sum_{n\le X}\frac{\log^αd_n}{d_n}…

math.NT2018★ 4 cited

On the distribution of rank and crank statistics for integer partitions

Nian Hong Zhou

Let $k$ be a positive integer and $m$ be an integer. Garvan's $k$ -rank $N_{k} (m, n)$ is the number of partitions of $n$ into at least $(k - 1)$ successive Durfee squares with $k$ -rank e…