N. Zhou

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20172021

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math.NT2021

Partitions into Piatetski-Shapiro sequences

Nian Hong Zhou, Ya-Li Li

Let $κ$ be a positive real number and $m \in N \cup {\infty}$ be given. Let $p_{κ, m} (n)$ denote the number of partitions of $n$ into the parts from the Piatestki-Shapiro se…

math.NT2020

On the infinite Borwein product raised to a positive real power

Michael J. Schlosser, Nian Hong Zhou

In this paper, we study properties of the coefficients appearing in the $q$ -series expansion of $\prod_{n \geq 1} [(1 - q^{n}) / (1 - q^{p n})]^{δ}$ , the infinite Borwein product for an arbitrar…

math.NT2020

Partitions into Beatty sequences

Nian Hong Zhou

Let $α > 1$ be an irrational number. We establish asymptotic formulas for the number of partitions of $n$ into summands and distinct summands, chosen from the Beatty sequence $(\lflo…

math.NT2019

Counting the number of solutions to certain infinite Diophantine equations

Nian Hong Zhou, Yalin Sun

Let $r, v, n$ be positive integers. This paper investigate the number of solutions $s_{r, v} (n)$ of the following infinite Diophantine equations $$ n=1^{r}\cdot |k_{1}|^{v}+2^{r}\cd…

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

Note on partitions into polynomials with number of parts in an arithmetic progression

Nian Hong Zhou

Let $f : Z_{+} \to Z_{+}$ be a polynomial with the property that corresponding to every prime $p$ there exists an integer $ℓ$ such that $p ∤ f (ℓ)$ . In…

Partitions into Piatetski-Shapiro sequences

On the infinite Borwein product raised to a positive real power

Partitions into Beatty sequences

Counting the number of solutions to certain infinite Diophantine equations

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

Note on partitions into polynomials with number of parts in an arithmetic progression

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