On Veech's proof of Sarnak's theorem on the Möbius flow

2017/11/15 by El Houcein El Abdalaoui, Abdalaoui, el Houcein el · 1 citation
Mathematics · #11N37 #37A45 #37B10 #54H10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1711.06326

openalex publication_date 2017/11/15 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28

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.

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• On the spectral analysis of dynamical Möbius-Sarnak process and topological entropy of Möbius fonction

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