Jinjiang Li

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math.NT2024

On Waring-Goldbach problem for one square and seventeen fifth powers of primes

Min Zhang, Jinjiang Li, Fei Xue

In this paper, it is established that every sufficiently large positive integer $n$ subject to $n \equiv 0 (mod 2)$ can be represented as a sum of one square of prime and seventeen fif…

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…

math.NT2023

On Chen's theorem over Piatetski-Shapiro type primes and almost-primes

Jinjiang Li, Fei Xue, Min Zhang

In this paper, we establish a new mean value theorem of Bombieri-Vinogradov type over Piatetski-Shapiro sequence. Namely, it is proved that for any given constant $A > 0$ and any suf…

math.NT2016

On the Sum of Divisors of Mixed Powers

Jinjiang Li, Min Zhang

Let $d (n)$ denote the Dirichlet divisor function. Define \begin{equation*} \mathcal{S}_{k}(x)=\sum_{\substack{1\leqslant n_1,n_2,n_3 \leqslant x^{1/2} \\ 1\leqslant n_4\leqslant x^…