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

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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.
5 pages

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Number Theory, Algebraic Geometry, 11T99; 14G10

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http://salesiana.dossiersoluciones.com/handle/123456789/155417

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.3200
 http://arxiv.org/abs/0802.3200

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arXiv