Lirui Jia

activity

20152025

most citedA congruence involving harmonic sums modulo

p^{α} q^{β}

8 citations · 9 across the 5 of their papers we have counts for

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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.NT2019

On the divisor problem with congruence conditions

Lirui Jia, Wenguang Zhai, Tianxin Cai

Let $d (n; r_{1}, q_{1}, r_{2}, q_{2})$ be the number of factorization $n = n_{1} n_{2}$ satisfying $n_{i} \equiv r_{i} (mod q_{i})$ ( $i = 1, 2$ ) and $Δ (x; r_{1}, q_{1}, r_{2}, q_{2})$ be the error term of the summ…

math.NT2016

On the Sign Changes of a Weighted Divisor Problem

Lirui Jia, Tianxin Cai, Wenguang Zhai

Let $S (x; \frac{a _{1}}{q _{1}}, \frac{a _{2}}{q _{2}}) = \sum^{'}_{mn \leq x} cos (2 π m \frac{a _{1}}{q _{1}}) sin (2 π n \frac{a _{2}}{q _{2}})$ with $x\geq q_1q_2, 1\leq a_i\leq…

math.NT2016★ 1 cited

A Weighted Divisor Problem

Lirui Jia, Wenguang Zhai

We study a weighted divisor function $mn \leq x \sum^{'} cos (2 π m θ_{1}) sin (2 π n θ_{2})$ , where $θ_{i} (0 < θ_{i} < 1)$ is a rational number. By connecting it with the divisor pro…

math.NT2015★ 8 cited

A congruence involving harmonic sums modulo $p^{α} q^{β}$

Tianxin Cai, Zhongyan Shen, Lirui Jia

In 2014, Wang and Cai established the following harmonic congruence for any odd prime $p$ and positive integer $r$ , \begin{equation*} Z(p^{r})\equiv-2p^{r-1}B_{p-3} ~(\bmod ~ p^{r}…