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Hai-Liang Wu

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Preprint Sep 2026

Arithmetic progressions in dense subsets of primitive elements of finite fields

Let $p$ be a prime and let $\mathcal{P}_p$ be the set of primitive elements of $\mathbb{F}_p$. Inspired by the work of Cohen, Oliveira e Silva and Trudgian on consecutive primitive elements, and by the work of Chang on arithmetic progressions in multiplicative subgroups of finite fields, in this paper, using estimates...

Hai-Liang Wu · 0 citations

Preprint Aug 2026

Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields

Let $f(t)\in\mathbb{Z}[t]$ be a nonconstant polynomial with nonzero discriminant and let $k\ge2$ be an integer. Inspired by the work of Alon and Bourgain, for sufficiently large prime $p\equiv1\pmod{k}$, we study cyclic orderings of subsets $A\subseteq \mathbb{F}_p$ for which $ f(a_i+a_{i+1})$ is a nonzero $k$-th power...

Hai-Liang Wu, He-Xia Ni · 0 citations