Author

Xiao-Hui Yan

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Preprint Oct 2026

On a conjecture on Romanoff type representations

Let $r_1,\ldots,r_t$ be positive integers, and let $\mathcal A$ be the set of integers of the form $2^{k_1^{r_1}}+\cdots+2^{k_t^{r_t}}$, where $k_1,\ldots,k_t$ are positive integers. For any positive integer $n$, let $r(n)$ be the number of representations $n=p+a$ with $p$ an odd prime and $a\in \mathcal A$. We prove t...

Xiao-Hui Yan · 0 citations

Preprint Sep 2026

A problem of Yang and Chen on weighted representation functions

Let $\mathbb N$ denote the set of nonnegative integers. For an integer $k>1$ and a set $A\subseteq\mathbb N$, let $R_{1,k}(A,n)$ denote the number of solutions of $n=a_1+ka_2$ with $a_1,a_2\in A$. For integers $k>1$ and $t\ge1$, Yang and Chen defined $f_k(t)$ to be the number of sets $A\subseteq\mathbb N$ for which \[...

Shuang-Shuang Li, Ya-Ting Xu, Xiao-Hui Yan · 0 citations