Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence qrt n modulo 1
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If you have a question about this talk, please contact Mustapha Amrani.
Interactions between Dynamics of Group Actions and Number Theory
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 1dimensional 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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