论文标题
有关Korobov的$ P $ set的定期$ L_2 $ -Discrepancy的注释
A note on the periodic $L_2$-discrepancy of Korobov's $p$-sets
论文作者
论文摘要
我们研究了$ d $维圆环中的点套装的定期$ l_2 $ discrepancy。这种差异与移动点集的根平方$ l_2 $ disccrepancy与Diaphony的概念密切相关，并且与Cubature公式的最坏情况下，在Sobolev sobolev sobolev sobolev sobles sobles soplace sobles soplace soplace sobolev spoolsive中的误差最坏。 在差异理论中，许多结果基于平均论点。为了使这些结果与应用相关，需要``平均''差异的点集明确构造。在我们的主要结果中，我们研究了Korobov的$ P $集，并表明这一点集具有定期的$ L_2 $ - 列表的平均订单。该结果与诺瓦克和沃尼亚科夫斯基的一个公开问题有关。
We study the periodic $L_2$-discrepancy of point sets in the $d$-dimensional torus. This discrepancy is intimately connected with the root-mean-square $L_2$-discrepancy of shifted point sets, with the notion of diaphony, and with the worst case error of cubature formulas for the integration of periodic functions in Sobolev spaces of mixed smoothness. In discrepancy theory many results are based on averaging arguments. In order to make such results relevant for applications one requires explicit constructions of point sets with ``average'' discrepancy. In our main result we study Korobov's $p$-sets and show that this point sets have periodic $L_2$-discrepancy of average order. This result is related to an open question of Novak and Woźniakowski.
