{"paper":{"title":"Uniformizer of the False Tate Curve Extension of $\\mathbb{Q}_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Shanwen Wang, Yijun Yuan","submitted_at":"2020-09-21T12:30:26Z","abstract_excerpt":"Let $p\\geq 3$ be a prime number. In this article, we study the canonical expansion of the primitive $p^n$-th root of unity $\\zeta_{p^n}$ in $p$-adic Mal'cev-Neumann field $\\mathbb{L}_p$ for $n\\geq 1$. More precisely, we give the explicit formula for the first $\\aleph_0$ terms of the expansion of $\\zeta_{p^n}$ and as an application, we use it to construct a uniformizer of $K_{2,m}=\\mathbb{Q}_p\\left(\\zeta_{p^2},p^{1/p^m}\\right)$ with $m\\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.09807","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/2009.09807/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"}