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 study the restriction of the Fourier transform to quadratic surfaces invector spaces over finite fields. In two dimensions, we obtain the sharp resultby considering the sums of arbitrary two elements in the subset of quadraticsurfaces on two dimensional vector spaces over finite fields. For higherdimensions, we estimate the decay of the Fourier transform of thecharacteristic functions on quadratic surfaces so that we obtain theTomas-Stein exponent. Using incidence theorems, we also study the extensiontheorems in the restricted settings to sizes of sets in quadratic surfaces.Estimates for Gauss and Kloosterman sums and their variants play an importantrole.

Extension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields