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

Tim Browning, Ilya Vinogradov

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
198 Downloads (Pure)

Abstract

Let G = SL(2, R) n R2 and Γ = SL(2, Z) n Z2. 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 convergence of the gap distribution of √
n mod 1.
Original languageEnglish
Pages (from-to)563-584
Number of pages22
JournalJournal of the London Mathematical Society
Volume83
Issue number4
Early online date24 May 2016
DOIs
Publication statusPublished - 1 Oct 2016

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