论Veech关于Möbius流上Sarnak定理的证明
动力系统
2022-09-16 v5 数论
摘要
我们给出Veech关于Möbius流上Sarnak定理的证明，该定理表明Möbius流上存在唯一的容许测度。作为推论，借助Tao的对数定理（其断言对数Sarnak猜想等价于对数Chowla猜想），我们得到Sarnak猜想等价于Chowla猜想；此外，若偶对数Sarnak猜想成立，则存在对数密度为1的子列，沿该子列Chowla猜想成立，即Möbius函数是拟泛的。
引用
@article{arxiv.1711.06326,
title = {On Veech's proof of Sarnak's theorem on the M\"{o}bius flow},
author = {el Houcein el Abdalaoui},
journal= {arXiv preprint arXiv:1711.06326},
year = {2022}
}
备注
11 pages. Some misprints are corrected, the proof of the main result with more details is reorganized. We further add some results and questions from the unpublished lecture notes and preprint (May 6, 2016) of W. Veech. I add also email from Veech sent March 11, 2016 in which he mentioned to me "there is only four persons in the world who has a copy of his notes including me."