### Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1

**Vinogradov, I ***(University of Bristol)*

Wednesday 18 June 2014, 14:30-15:30

Seminar Room 1, Newton Institute

#### Abstract

Let G=SL(2,\R)\ltimes R^2 and Gamma=SL(2,Z)\ltimes Z^2. Building on
recent work of Strombergsson we prove a rate of equidistribution for the
orbits of a certain 1-dimensional unipotent flow of Gamma\G, which projects to
a closed horocycle in the unit tangent bundle to the modular surface. We use
this to answer a question of Elkies and McMullen by making effective the
convergence of the gap distribution of sqrt n mod 1.

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