Jean Bourgain, Peter Sarnak and Tamar Ziegler. Distjointness of Mobius from horocycle flows
We formulate and prove a finite version of Vinogradov's bilinear sum inequality. We use it together with Ratner's joinings theorems to prove that the Mobius function is disjoint from discrete horocycle flows on Γ \ SL2(ℝ). .