On Veech's proof of Sarnak's theorem on the Möbius flow
arXiv:1711.06326
Abstract
We present Veech's proof of Sarnak's theorem on the Möbius flow which say that there is a unique admissible measure on the Möbius flow. As a consequence, we obtain that Sarnak's conjecture is equivalent to Chowla conjecture with the help of Tao's logarithmic Theorem which assert that the logarithmic Sarnak conjecture is equivalent to logaritmic Chowla conjecture, furthermore, if the even logarithmic Sarnak's conjecture is true then there is a subsequence with logarithmic density one along which Chowla conjecture holds, that is, the Möbius function is quasi-generic.
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 We further add some results and questions from the unpublished lecture notes and preprint (May 6, 2016) of W. Veech.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."