Fei Xue

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math.NT2025

On Higher-Power Moments of $I^_{a} (x)$ 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*} Î_{a}(x)=\sideset{}{'}\sum_{n\leq x} Ï_a(n)-Î¶(1-a)x-\frac{Î¶(1+a)}{1+a}x^{1+a}+\frac{1}{2}Î¶(-a). \end{equation*} In…

math.NT2024

Almost primes of the form $[p^{1/ I^^{3}}]$

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 $0.989 < I^^{3} < 1$ , there exist infini…

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

Almost primes of the form [p1/I^3]

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

Almost primes of the form $[p^{1/ I^^{3}}]$