%0 Journal Article
%T On Katz's bound for number of elements with given trace and norm
%A Marko Moisio
%A Daqing Wan
%J Mathematics
%D 2008
%I arXiv
%X In this note an improvement of the Katz's bound on the number of elements in a finite field with given trace and norm is given. The improvement is obtained by reducing the problem to estimating the number of rational points on certain toric Calabi-Yau hypersurface, and then to use detailed cohomological calculations by Rojas-Leon and the second author for such toric hypersurfaces.
%U http://arxiv.org/abs/0802.3200v1