N. Zhou

activity

20172019

collaborators

4 papers

math.NT2019

On the average sum of the $k$ -th divisor function over values of quadratic polynomials

Kostadinka Lapkova, Nian Hong Zhou

Let $F (x) \in Z [x_{1}, x_{2}, \dots, x_{n}]$ be a quadratic polynomial in $n \geq 3$ variables with a nonsingular quadratic part. Using the circle method we derive an asymptotic…

math.NT2019

Uniform asymptotic formulas of restricted bipartite partitions

Nian Hong Zhou

In this paper, we investigate $π (m, n)$ , the number of partitions of the \emph{bipartite number} $(m, n)$ into \emph{steadily decreasing} parts, introduced by L.Carlitz ['A problem i…

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.NT2017

Asymptotic formulae for Eulerian series

Nian Hong Zhou

Let $(a; q)_{\infty}$ be the $q$ -Pochhammer symbol and $li_{2} (x)$ be the dilogarithm function. Let $\prod_{α, β, γ}$ be a finite product with every triple $(α,β,γ)\in(\mathbb{…

On the average sum of the k-th divisor function over values of quadratic polynomials

Uniform asymptotic formulas of restricted bipartite partitions

Proof of a conjecture of Farkas and Kra

Asymptotic formulae for Eulerian series

On the average sum of the $k$ -th divisor function over values of quadratic polynomials