Fei Xue

activity

20172025

collaborators

7 papers

math.NT2025

On Higher-Power Moments of $Δ_{a} (x)$ for $- 1/2 < a < 0$

Yi Cai, Jinjiang Li, Yankun Sui +2

Let $- 1/2 < a < 0$ be a fixed real number and \begin{equation*} Δ_{a}(x)=\sideset{}{'}\sum_{n\leq x} σ_a(n)-ζ(1-a)x-\frac{ζ(1+a)}{1+a}x^{1+a}+\frac{1}{2}ζ(-a). \end{equation*} In this…

math.NT2024

Almost primes of the form $[p^{1/ γ}]$

Fei Xue, Jinjiang Li, Min Zhang

Let $P_{r}$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that, for $0.989 < γ < 1$ , there exist infinit…

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

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.NT2021

On the distribution of $α p^{2}$ modulo one with prime $p$ of a special form

Fei Xue, Jinjiang Li, Min Zhang

Let $P_{r}$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that for $α\in\mathbb{R}\backslash\mathbb{…

math.NT2020

An Additive Problem over Piatetski-Shapiro Primes and Almost-primes

Jinjiang Li, Min Zhang

Let $P_{r}$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, we establish a theorem of Bombieri-Vinogradov type for…

math.NT2017

On the Waring-Goldbach Problem for One Square and Five Cubes

Jinjiang Li, Min Zhang

Let $P_{r}$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even int…

On Higher-Power Moments of Δa​(x) for −1/2<a<0

Almost primes of the form [p1/γ]