论文标题
在Proinov的下限
On Proinov's lower bound for the diaphony
论文作者
论文摘要
1986年，普罗内诺夫（Proinov）为D维单位立方体中有限和无限序列的di魔发表了明确的下限。据我们所知，这些结果的证据才到目前为止，只有在保加利亚人写的Proinov专着。我们论文的第一个贡献是为Proinov的英语证明提供自我包含的版本。在此过程中，我们使用Hinrichs和Markhasin的最新和校正结果改善了渐近常数。最后，作为主要结果，我们使用Proinov的方法来以类似的方式为有限和无限序列的二元di魔而言明确的下限。
In 1986, Proinov published an explicit lower bound for the diaphony of both finite and infinite sequences of points in the d-dimensional unit cube. To the best of our knowledge, the proofs of these results were so far only available in a monograph of Proinov written in Bulgarian. The first contribution of our paper is to give a self contained version of Proinov's proof in English. Along the way, we improve the asymptotic constants using recent and corrected results of Hinrichs and Markhasin. Finally, as a main result, we use the method of Proinov to derive an explicit lower bound for the dyadic diaphony of finite and infinite sequences in a similar fashion.
