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Around Sziklai's conjecture on the number of points of a plane curve over a finite fieldopen access
- Authors
- Homma, Masaaki; Kim, Seon Jeong
- Issue Date
- Aug-2009
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Plane curve; Finite field; Rational point
- Citation
- FINITE FIELDS AND THEIR APPLICATIONS, v.15, no.4, pp 468 - 474
- Pages
- 7
- Indexed
- SCIE
SCOPUS
- Journal Title
- FINITE FIELDS AND THEIR APPLICATIONS
- Volume
- 15
- Number
- 4
- Start Page
- 468
- End Page
- 474
- ISSN
- 1071-5797
1090-2465
- Abstract
- This paper has double purposes. One of them is to give a new bound on the number of points of a plane curve of degree d over a finite field that meets Sziklai's conjectural bound at d = q + 1. An example shows that this bound is sharp for d = q + 1. The second one is to Study an example against that conjecture for q = d = 4. This curve also shows the sharpness of our bound. (C) 2009 Elsevier Inc. All rights reserved.
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