{"date_published":"2016-05-24T00:00:00Z","date_created":"2018-12-11T11:45:29Z","issue":"1","doi":"10.1112/jlms/jdw025","title":"Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1","intvolume":"        94","publisher":"John Wiley and Sons Ltd","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","last_name":"Browning","full_name":"Timothy Browning","first_name":"Timothy D"},{"full_name":"Vinogradov, Ilya","first_name":"Ilya","last_name":"Vinogradov"}],"publication_status":"published","day":"24","date_updated":"2021-01-12T06:58:33Z","quality_controlled":0,"extern":1,"_id":"261","abstract":[{"lang":"eng","text":"Let G = SL(2, R) ⋉R2 and Γ = SL(2, Z) ⋉Z2. Building on recent work of Strömbergsson, we prove a rate of equidistribution for the orbits of a certain one-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."}],"status":"public","type":"journal_article","publist_id":"7641","month":"05","acknowledgement":"The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreements 291147 and 306457.","volume":94,"year":"2016","publication":"Journal of the London Mathematical Society","page":"61 - 84","citation":{"chicago":"Browning, Timothy D, and Ilya Vinogradov. “Effective Ratner Theorem for SL (2, R) ⋉R2 and Gaps in √n modulo 1.” <i>Journal of the London Mathematical Society</i>. John Wiley and Sons Ltd, 2016. <a href=\"https://doi.org/10.1112/jlms/jdw025\">https://doi.org/10.1112/jlms/jdw025</a>.","short":"T.D. Browning, I. Vinogradov, Journal of the London Mathematical Society 94 (2016) 61–84.","apa":"Browning, T. D., &#38; Vinogradov, I. (2016). Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1. <i>Journal of the London Mathematical Society</i>. John Wiley and Sons Ltd. <a href=\"https://doi.org/10.1112/jlms/jdw025\">https://doi.org/10.1112/jlms/jdw025</a>","ista":"Browning TD, Vinogradov I. 2016. Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1. Journal of the London Mathematical Society. 94(1), 61–84.","ama":"Browning TD, Vinogradov I. Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1. <i>Journal of the London Mathematical Society</i>. 2016;94(1):61-84. doi:<a href=\"https://doi.org/10.1112/jlms/jdw025\">10.1112/jlms/jdw025</a>","ieee":"T. D. Browning and I. Vinogradov, “Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1,” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 1. John Wiley and Sons Ltd, pp. 61–84, 2016.","mla":"Browning, Timothy D., and Ilya Vinogradov. “Effective Ratner Theorem for SL (2, R) ⋉R2 and Gaps in √n modulo 1.” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 1, John Wiley and Sons Ltd, 2016, pp. 61–84, doi:<a href=\"https://doi.org/10.1112/jlms/jdw025\">10.1112/jlms/jdw025</a>."}}