arXiv subjects

Yankun Sui

Publications and source records attributed to Yankun Sui.

3 recordsLinked to original sources

arXiv2025

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

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 paper, we investigate the higher--power moments of $Δ_a(x)$ and give the corresponding asymptotic formula for the integral $\int_{1}^{T}Δ_a^k(x)\mathrm{d}x$, which constitutes an improvement upon the previous result of Zhai [9] for $k=3,4,5$ and an enlargement of the upper bound of $k$ to $7$.

math.NT↗

arXiv2025

Cubic Waring-Goldbach problem with Piatetski-Shapiro primes

In this paper, it is proved that, for $γ\in(\frac{317}{320},1)$, every sufficiently large odd integer can be written as the sum of nine cubes of primes, each of which is of the form $[n^{1/γ}]$. This result constitutes an improvement upon the previous result of Akbal and Güloğlu [1].

math.NT↗

arXiv2025

On the number of subgroups of the group $\mathbb{Z}_{m_{1}} \times \mathbb{Z}_{m_{2}}$ with $m_{1}m_{2}\leq x$ such that $m_{1}m_{2}$ is a $k$-th power

Let ${\Bbb Z}_{m}$ be the additive group of residue classes modulo $m$ and $s(m_{1},m_{2})$ denote the number of subgroups of the group ${\Bbb Z}_{m_{1}}\times {\Bbb Z}_{m_{2}}$, where $m_{1}$ and $m_{2}$ are arbitrary positive integers. We consider sums of type $\sum\limits_{\substack{m_{1}m_{2}\leq x \\ m_{1}m_{2}\in N_{k}}}s(m_{1},m_{2})$, where $N_{k}$ is the set of $k$-th power of natural numbers. In particular, we deduce asymptotic formulas with $k=2$ and $k=3$.

math.NT↗