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An elementary bound for the number of points of a hypersurface over a finite field
- Authors
- Homma, Masaaki; Kim, Seon Jeong
- Issue Date
- Mar-2013
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Hypersurface; Finite field; Number of points
- Citation
- FINITE FIELDS AND THEIR APPLICATIONS, v.20, pp 76 - 83
- Pages
- 8
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- FINITE FIELDS AND THEIR APPLICATIONS
- Volume
- 20
- Start Page
- 76
- End Page
- 83
- ISSN
- 1071-5797
1090-2465
- Abstract
- We establish an upper bound for the number of points of a hypersurface without a linear component over a finite field, which is analogous to the Sziklai bound for a plane curve. Our bound is the best one for irreducible hypersurfaces that is linear on their degrees, because, for each finite field, there are at least two irreducible hypersurfaces of different degrees that reach our bound. (C) 2012 Elsevier Inc. All rights reserved.
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