Certain results on the Möbius disjointness conjecture

Abstract: We study certain aspects of the Möbius randomness principle and more specifically the Möbius disjointness conjecture of P. Sarnak. In paper A we establish this conjecture for all orientation preserving circle homeomorphisms and continuous interval maps of zero entropy. In paper B we show, that for all subshifts of finite type with positive topological entropy the Möbius disjointness does not hold. In paper C we study a class of three-interval exchange maps arising from a paper of Bourgain and estimate its Hausdorff dimension. In paper D we consider the Chowla and Sarnak conjectures and the Riemann hypothesis for abstract sequences and study their relationship.