{"paper":{"title":"Lattices over Polynomial Rings and Applications to Function Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jens-Dietrich Bauch","submitted_at":"2016-01-07T00:42:04Z","abstract_excerpt":"This paper deals with lattices $(L,\\Vert~\\Vert)$ over polynomial rings, where $L$ is a finitely generated module over $k[t]$, the polynomial ring over the field $k$ in the indeterminate $t$, and $\\Vert~\\Vert$ is a discrete real-valued length function on $L\\otimes_{k[t]}k(t)$. A reduced basis of $(L,\\Vert~\\Vert)$ is a basis of $L$ whose vectors attain the successive minima of $(L,\\Vert~\\Vert)$. We develop an algorithm which transforms any basis of $L$ into a reduced basis of $(L,\\Vert~\\Vert)$. By identifying a divisor $D$ of an algebraic function field with a lattice $(L,\\Vert~\\Vert)$ over a po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01361","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"}