Extension theorems for spheres in the finite field setting
By Alex Iosevich, Doowon Koh. 2007
66 citations recorded by the source corpus.
Abstract In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields. In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a subset of spheres. As a result, we improve the Tomas-Stein exponents, previous results by the authors in [Iosevich and Koh, Illinois J. of Mathematics: 2008]. The analytic approach and the explicit formula for Fourier transform of the characteristic function on spheres play an important role to get good bounds for exponential sums.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/529e7c04b525afea0321c08b9933f2c71a1ed7c7
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- New Restriction Estimates for the 3-d Paraboloid over Finite Fields (2013, background): “In the finite field setting, the restriction phenomenon has already received a fair amount of attention, see [6], [7], [8] [12], [13], [14].”