A reduction for counting the number of zeros of general diagonal equation over finite fields
A reduction for counting the number of zeros of general diagonal equation over finite fields
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DOI：
10.1016/j.ffa.2005.07.001
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发表时间：
2006-11
期刊：
影响因子：
--
通讯作者：
W. Cao;Qi Sun
中科院分区：
文献类型：
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作者：
W. Cao;Qi Sun
我们提供了一种计算有限域上所谓的一般对角线方程的零个数的有效约简，其形式为[公式：见文本]。这推广了形式为[公式：见文]的简单对角方程和形式为a1x11⋯x1l+⋯+arxr1⋯xrl=0的l-线性方程的相应结果。此外，我们还证明了Chevalley-Warning-Ax-Katz型估计可以通过我们的约简得到改进。
We provide an efficient reduction for counting the number of zeros of the so-called general diagonal equation over finite fields, which is of the form [Formula: see text] . This generalizes the corresponding results for the simple diagonal equation of the form [Formula: see text] and the l-linear equation of the form a1x11⋯x1l+⋯+arxr1⋯xrl=0. Furthermore, we show that the Chevalley–Warning–Ax–Katz type estimates can be improved in the cases of general diagonal equations by our reduction.