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

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

2008-02-21

arxiv.org/abs/0802.3200v1

Mathematics

Number Theory

5 pages

Scientific paper

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.

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