{"paper":{"title":"Diophantine exponents for standard linear actions of $\\mathrm{SL}_2$ over discrete rings in $\\mathbb{C}$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"L. Singhal","submitted_at":"2015-09-04T16:24:42Z","abstract_excerpt":"We give upper and lower bounds for various Diophantine exponents associated with the standard linear actions of $\\mathrm{SL}_2 ( \\mathcal{O}_K )$ on the punctured complex plane $\\mathbb{C}^2 \\setminus \\{ \\mathbf{0} \\}$, where $K$ is a number field whose ring of integers $\\mathcal{O}_K$ is discrete and within a unit distance of any complex number. The results are similar to those of Laurent and Nogueira for $\\mathrm{SL}_2 ( \\mathbb{Z} )$ action on $\\mathbb{R}^2 \\setminus \\{ \\mathbf{0} \\}$ albeit for us, uniformly nice bounds are obtained only outside of a set of null measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01521","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}