Extension Theorems for Spheres in the Finite Field Setting
Classical Analysis and ODEs
2018-11-20 v2 Combinatorics
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, 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.
Keywords
Cite
@article{arxiv.0712.1627,
title = {Extension Theorems for Spheres in the Finite Field Setting},
author = {Alex Iosevich and Doowon Koh},
journal= {arXiv preprint arXiv:0712.1627},
year = {2018}
}
Comments
28 pages, 3 figures, published version