{"paper":{"title":"Eisenstein-Dumas criterion and the action of $2\\times 2$ nonsingular triangular matrices on polynomials in one variable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Martin Juras","submitted_at":"2015-05-28T10:31:54Z","abstract_excerpt":"Let $K$ be a valued field (in general $K$ is not heselian) with valuation $v$ and $A(x)\\in K[x]$ be a polynomial of degree $n$. We find necessary and sufficient conditions for the existence of the elements $s,t,u\\in K$, $s\\neq 0\\neq u$, such that at least one of the polynomials $u^nA(\\frac{sx+t}{u})$, $(tx+u)^nA(\\frac{sx}{tx+u})$, $(ux)^nA(\\frac{tx+s}{ux})$ or $(ux+t)^nA(\\frac{s}{ux+t})$ is an Eisenstein-Dumas polynomial at $v$, provided that the characteristic of the residue field of $v$ does not divide $n$. Furthermore, we show that if the orbit $A(x)GL(2,K)$ contains an Eisenstein-Dumas pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07633","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"}