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

We prove that the finite field Fourier extension operator for the paraboloidis bounded from $L^2\to L^r$ for $r\geq \frac{2d+4}{d}$ in even dimensions$d\ge 8$, which is the optimal $L^2$ estimate. For $d=6$ we obtain the optimalrange $r> \frac{2d+4}{d}=8/3$, apart from the endpoint. For $d=4$ we improvethe prior range of $r>16/5=3.2$ to $r\geq 28/9=3.111\ldots$, compared to theconjectured range of $r\geq3$. The key new ingredient is improved additiveenergy estimates for subsets of the paraboloid.

Finite field restriction estimates for the paraboloid in high even dimensions