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On Katz's bound for the number of elements with given trace and norm
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Marko Moisio
Published/Copyright:
November 23, 2009
Abstract
In this note an improvement of 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 hypersurfaces, and then to use detailed cohomological calculations by Rojas-Leon and the second author for such toric hypersurfaces.
Received: 2008-02-21
Published Online: 2009-11-23
Published in Print: 2010-January
© Walter de Gruyter Berlin · New York 2010
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- Waring's problem in function fields
- On Katz's bound for the number of elements with given trace and norm
- Free evolution on algebras with two states
- Decomposition of residue currents
- Free holomorphic automorphisms of the unit ball of B(ℋ)n
- Morrey estimates and Hölder continuity for solutions to parabolic equations with entropy inequalities
- Surgery formula for Seiberg–Witten invariants of negative definite plumbed 3-manifolds
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Articles in the same Issue
- Waring's problem in function fields
- On Katz's bound for the number of elements with given trace and norm
- Free evolution on algebras with two states
- Decomposition of residue currents
- Free holomorphic automorphisms of the unit ball of B(ℋ)n
- Morrey estimates and Hölder continuity for solutions to parabolic equations with entropy inequalities
- Surgery formula for Seiberg–Witten invariants of negative definite plumbed 3-manifolds
- Mld's vs thresholds and flips
