Polynomial Values in Affine Subspaces in Finite Fields

Alina Ostafe

Published 2014-10-06Version 1

In this paper we obtain new results about polynomial values falling in affine subspaces of finite fields, improving and generalising previous known results, but also extending the range of such results to polynomials of degrees higher than the characteristic of the field. Such results have immediate consequences to intersection of orbits with affine subspaces, but also for the Waring's problem in affine subspaces. We also obtain estimates for a certain new type of exponential sums.