{"paper":{"title":"Elementary resolution of a family of quartic Thue equations over function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ana Jurasi\\'c, Clemens Fuchs, Roland Paulin","submitted_at":"2014-12-10T07:30:52Z","abstract_excerpt":"We consider and completely solve the parametrized family of Thue equations \\begin{eqnarray*}X(X-Y)(X+Y)(X-\\lambda Y)+Y^4=\\xi,\\end{eqnarray*} where the solutions $x,y$ come from the ring $\\mathbb{C}[T]$, the parameter $\\lambda\\in\\mathbb{C}[T]$ is some non-constant polynomial and $0\\neq\\xi\\in\\mathbb{C}$. It is a function field analogue of the family solved by Mignotte, Peth\\H{o} and Roth in the integer case. A feature of our proof is that we avoid the use of height bounds by considering a smaller relevant ring for which we can determine the units more easily. Because of this, the proof is short "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3216","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":""},"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"}