New Restriction Estimates for the 3-d Paraboloid over Finite Fields

Mark Lewko

Published 2013-02-27, updated 2016-05-30Version 2

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.