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

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Interactions between Dynamics of Group Actions and Number Theory

Let G=SL(2,R)ltimes R2 and Gamma=SL(2,Z)ltimes Z2. Building on recent work of Strombergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of GammaG, 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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