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

Presented by: 
I Vinogradov University of Bristol
Date: 
Wednesday 18th June 2014 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons