In [3], we derived three results in additive combinatorics for function fields. The proofs of these results depended on a recent bound for the large sieve with sparse sets of moduli for function fields by the first and third-named authors in [1]. Unfortunately, they discovered an error in this paper and demonstrated in [2] that this result cannot hold in full generality. In the present paper, we formulate a plausible conjecture under which the said three results in [3] remain true and the method of proof goes through using the same arguments. However, these results are now only conditional and still await a full proof.

中文翻译：

---

更正：函数域的可分性问题

在[3]中，我们在函数域的加法组合中推导出三个结果。这些结果的证明取决于 [1] 中的第一和第三作者最近对函数域的稀疏模集的大筛子的边界。不幸的是，他们在这篇论文中发现了一个错误，并在 [2] 中证明了这个结果不能完全通用。在本文中，我们提出了一个似是而非的猜想，在该猜想下，[3] 中的上述三个结果仍然成立，并且证明方法使用相同的论据。然而，这些结果现在只是有条件的，仍在等待完整的证明。