This paper corrects an error in the proof of Theorem 1.4 (3) of our earlier paper, . The error originally appeared in Heath-Brown's paper, , which invalidates the proof of Theorem 2 (iii) in that paper. In this paper, we use a new method to give a correct proof of Theorem 1.4 (3). The correction in this paper also fixes the proof of Theorem 2 (iii) in Heath-Brown's paper. The proof in this paper provides slightly stronger estimates for some of the inequalities that were used in .

中文翻译：

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对Chevalley-Warning定理的修正和进一步改进

本文纠正了我们早期论文定理 1.4 (3) 的证明中的错误。该错误最初出现在 Heath-Brown 的论文 中，导致该论文中定理 2 (iii) 的证明无效。在本文中，我们使用一种新的方法给出了定理1.4(3)的正确证明。本文的修正也修正了 Heath-Brown 论文中定理 2 (iii) 的证明。本文中的证明为 中使用的一些不等式提供了稍微更强的估计。