Effective Ratner theorem for SL(2, R)⋉R2 and gaps in n modulo 1

Abstract

Let G = SL(2, R) R 2 and Γ = SL(2, Z) Z 2. Building on recent work of Strömbergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Γ\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… (More)
DOI: 10.1112/jlms/jdw025

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