{"paper":{"title":"On Fourier asymptotics and effective equidistribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Shreyasi Datta, Subhajit Jana","submitted_at":"2024-07-16T17:58:40Z","abstract_excerpt":"We prove effective equidistribution of expanding horocycles in $\\mathrm{SL}_2(\\mathbb{Z})\\backslash\\mathrm{SL}_2(\\mathbb{R})$ with respect to various classes of Borel probability measures on $\\mathbb{R}$ having certain Fourier asymptotics. Our proof involves new techniques combining tools from automorphic forms and harmonic analysis.\n  In particular, for any Borel probability measure $\\mu$, satisfying $\\sum_{\\mathbb{Z}\\ni|m|\\leq X}|\\widehat{\\mu}(m)| = O\\left(X^{1/2-\\theta}\\right)$ with $\\theta>7/64,$ our result holds. This class of measures contains convolutions of $s$-Ahlfors regular measures"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.11961","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.11961/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}