{"paper":{"title":"On Hausdorff dimension in inhomogeneous Diophantine approximation over global function fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Fr\\'ed\\'eric Paulin, Seonhee Lim, Taehyeong Kim","submitted_at":"2021-12-08T06:50:24Z","abstract_excerpt":"In this paper, we study inhomogeneous Diophantine approximation over the completion $K_v$ of a global function field $K$ (over a finite field) for a discrete valuation $v$, with affine algebra $R_v$. We obtain an effective upper bound for the Hausdorff dimension of the set \\[ \\mathbf{Bad}_A(\\epsilon)=\\left\\{\\boldsymbol{\\theta}\\in K_v^{\\,m} : \\liminf_{(\\mathbf{p},\\mathbf{q})\\in\n  R_v^{\\,m} \\times R_v^{\\,n}, \\|\\mathbf{q}\\|\\to \\infty} \\|\\mathbf{q}\\|^n \\|A\\mathbf{q}-\\boldsymbol{\\theta}-\\mathbf{p}\\|^m \\geq \\epsilon \\right\\}, \\] of $\\epsilon$-badly approximable targets $\\boldsymbol{\\theta}\\in K_v^{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04144","kind":"arxiv","version":3},"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/2112.04144/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"}