Distjointness of Mobius from horocycle flows
Number Theory
2011-10-06 v1 Dynamical Systems
Abstract
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 $\Gamma \backslash SL_2(\mathbb{R}).
Keywords
Cite
@article{arxiv.1110.0992,
title = {Distjointness of Mobius from horocycle flows},
author = {Jean Bourgain and Peter Sarnak and Tamar Ziegler},
journal= {arXiv preprint arXiv:1110.0992},
year = {2011}
}