Fei Xue

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20172025

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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.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

On the distribution of αp2 modulo one with prime p of a special form

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

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

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

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