An elementary bound for the number of points of a hypersurface over a finite field
An elementary bound for the number of points of a hypersurface over a finite field
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有限域上超曲面点数的基本界限
DOI：
10.1016/j.ffa.2012.11.002
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. Homma and S. J. Kim
中科院分区：
文献类型：
--
作者：
Takeshi Harui;Jiryo Komeda;Akira Ohbuchi;M. Homma and S. J. Kim
我们建立了有限域上不含线性分量的超曲面的点数的上界，它类似于平面曲线的Sziklai界。我们的界是最好的一个不可约超曲面，是线性的，因为，对每个有限域，至少有两个不可约超曲面的不同程度，达到我们的界。
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.