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

Sur la preuve de Veech du théorème de Sarnak concernant le flot de Möbius

El Houcein El Abdalaoui (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Domaines: Systèmes dynamiques [math.DS]; Théorie des nombres [math.NT]; Combinatoire [math.CO]; Probabilités [math.PR]

El Houcein El Abdalaoui. On Veech's proof of Sarnak's theorem on the Möbius flow . 2018. ⟨hal-01632280v2⟩