{"paper":{"title":"Equidistribution of polynomial sequences in function fields: resolution of a conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\'er\\'emy Champagne, Th\\'ai Ho\\`ang L\\^e, Trevor D. Wooley, Yu-Ru Liu, Zhenchao Ge","submitted_at":"2025-12-18T03:11:48Z","abstract_excerpt":"Let $\\mathbb F_q$ be the finite field of $q$ elements having characteristic $p$, and denote by $\\mathbb K_\\infty=\\mathbb F_q((1/t))$ the field of formal Laurent series in $1/t$. We consider the equidistribution in $\\mathbb T=\\mathbb K_\\infty/\\mathbb F_q[t]$ of the values of polynomials $f(u)\\in \\mathbb K_\\infty [u]$ as $u$ varies over $\\mathbb F_q[t]$. Let $\\mathcal K$ be a finite set of positive integers, and suppose that $\\alpha_r\\in \\mathbb K_\\infty$ for $r\\in \\mathcal K\\cup \\{0\\}$. We show that the polynomial $\\sum_{r\\in \\mathcal K\\cup\\{0\\}}\\alpha_ru^r$ is equidistributed in $\\mathbb T$ wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.16118","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/2512.16118/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"}