English

On Katz's bound for number of elements with given trace and norm

Number Theory 2008-02-22 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.0802.3200,
  title  = {On Katz's bound for number of elements with given trace and norm},
  author = {Marko Moisio and Daqing Wan},
  journal= {arXiv preprint arXiv:0802.3200},
  year   = {2008}
}

Comments

5 pages

R2 v1 2026-06-21T10:14:51.622Z