Wenguang Zhai

activity

20232026

collaborators

6 papers

math.NT2026

A survey on moments of a class of error terms

Zhai Wenguang

This is a survey article on the moments of a class of error terms in analytic number theory. We begin by reviewing the moments of the Dirichlet divisor problem, and then review the…

math.NT2026

On the average number of subgroups of the group $Z_{n_{1}} \times Z_{n_{2}}$

Zhai Wenguang

Let $Z_{n}$ be the additive group of residue classes modulo $n .$ For any positive integers $n_{1}$ and $n_{2}$ , let $s (n_{1}, n_{2})$ and $c (n_{1}, n_{2})$ denote the number of subgrou…

math.NT2025

On the mean square of the error term for the number of lattice points in a two-dimensional area

Lirui Jia, Wenguang Zhai

Suppose $a, b$ are fixed algebraic numbers with $1 \leq a < b$ . Let $Δ_{a, b} (x)$ be the error term for the number of lattice points in a two-dimensional area $h^{a} r^{b} \leq x$ with $h,…

math.NT2024

A generalization of the Romanoff theorem

Yuchen Ding, Wenguang Zhai

Let $P$ be the set of primes and $N$ the set of positive integers. Let also $r_{1}, ..., r_{t}$ be positive real numbers and $R_{2} (r_{1}, ..., r_{t})$ the set of odd integers…

math.NT2023

On a conjecture of Ram\'ırez Alfons\'ın and Skałba II

Yuchen Ding, Wenguang Zhai, Lilu Zhao

Let $1 < c < d$ be two relatively prime integers and $g_{c, d} = c d - c - d$ . We confirm, by employing the Hardy--Littlewood method, a 2020 conjecture of Ram\'ırez Alfons\'ın and Skałba which…

math.NT2023

Primes in the intersection of two Piatetski-Shapiro sets

Xiaotian Li, Wenguang Zhai, Jinjiang Li

Let $π (x; γ_{1}, γ_{2})$ denote the number of primes $p$ with $p ⩽ x$ and $p = ⌊ n_{1}^{1/ γ_{1}} ⌋ = ⌊ n_{2}^{1/ γ_{2}} ⌋$ , where $⌊ t ⌋$ denotes the integer p…