New Restriction Estimates for the 3-d Paraboloid over Finite Fields
Classical Analysis and ODEs
2016-06-01 v2 Combinatorics
Abstract
We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain-Katz-Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid.
Keywords
Cite
@article{arxiv.1302.6664,
title = {New Restriction Estimates for the 3-d Paraboloid over Finite Fields},
author = {Mark Lewko},
journal= {arXiv preprint arXiv:1302.6664},
year = {2016}
}
Comments
19 pages, published version