Extension Theorems for Spheres in the Finite Field Setting

Details Extension Theorems for Spheres in the Finite Field Setting Extension Theorems for Spheres in the Finite Field Setting

2007-12-11

arxiv.org/abs/0712.1627v1

Mathematics

Classical Analysis and ODEs

28 pages, 3 figures

Scientific paper

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, our previous results. 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.

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