For a finite field with fixed and sufficiently large, we prove the existence of a primitive element outside of a set of many affine hyperplanes for and . This complements earlier results by Fernandes and Reis for . For the analogous result can be derived from a very recent bound on character sums of Iyer and Shparlinski. For the set consists only of a single element, and such a result is thus not possible.

中文翻译：

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有限域的本元[公式省略]避免 q = 4 和 q = 5 的仿射超平面

对于固定且足够大的有限域，我们证明 和 的一组许多仿射超平面之外存在一个本原元素。这补充了 Fernandes 和 Reis 的早期结果。因为类似的结果可以从 Iyer 和 Shparlinski 的字符和的最近界限中导出。因为该集合仅由单个元素组成，因此这样的结果是不可能的。