论 Vinogradov 均值定理：通过高效同余法实现的强对角行为
数论
2014-11-25 v3
摘要
我们改进了用于估计阶数为 的 Vinogradov 积分的高效同余法，其中 。以此方式，我们证明了当 时此类偶数矩的主要猜想，表明矩在此范围内表现出强对角行为。对于较大的 值也有改进，这些发现可应用于 Waring 问题中的渐近公式。
引用
@article{arxiv.1304.6917,
title = {On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing},
author = {Kevin Ford and Trevor D. Wooley},
journal= {arXiv preprint arXiv:1304.6917},
year = {2014}
}
备注
v3. 2013-12-18. We corrected the relation in the second display following (3.5) in the proof of Lemma 3.3, and corrected the argument leading from (5.1) to the 2nd display preceding (5.2) in the proof of Lemma 5.1. We rearranged the proof of Lemma 7.1 a bit, and corrected a number of very small typos. arXiv admin note: text overlap with arXiv:1112.0358, arXiv:1310.8447