English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Given $E \subseteq \mathbb{F}_q^d \times \mathbb{F}_q^d$, with the finitefield $\mathbb{F}_q$ of order $q$ and the integer $d \ge 2$, we define thetwo-parameter distance set as $\Delta_{d, d}(E)=\left\{\left(\|x_1-y_1\|,\|x_2-y_2\|\right) : (x_1,x_2), (y_1,y_2) \in E \right\}$. Birklbauer andIosevich (2017) proved that if $|E| \gg q^{\frac{3d+1}{2}}$, then $ |\Delta_{d,d}(E)| = q^2$. For the case of $d=2$, they showed that if $|E| \ggq^{\frac{10}{3}}$, then $ |\Delta_{2, 2}(E)| \gg q^2$. In this paper, wepresent extensions and improvements of these results.

On the two-parameter Erd\H{o}s-Falconer distance problem over finite fields