Distjointness of Mobius from horocycle flows
Jean Bourgain, Peter Sarnak, Tamar Ziegler
TL;DR
This paper proves that the Mobius function is disjoint from discrete horocycle flows using a finite version of Vinogradov's inequality and Ratner's joinings theorems, advancing understanding in ergodic theory and number theory.
Contribution
It introduces a finite version of Vinogradov's bilinear sum inequality and applies Ratner's joinings theorems to establish disjointness results.
Findings
Mobius function is disjoint from discrete horocycle flows.
Finite Vinogradov inequality is formulated and proved.
Application of Ratner's joinings theorems to ergodic flows.
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}).
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Nonlinear Partial Differential Equations