{"paper":{"title":"Generation of the Symmetric Field by Newton Polynomials in prime Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maurizio Monge","submitted_at":"2009-03-18T16:13:36Z","abstract_excerpt":"Let $N_m = x^m + y^m$ be the $m$-th Newton polynomial in two variables, for $m \\geq 1$. Dvornicich and Zannier proved that in characteristic zero three Newton polynomials $N_a, N_b, N_c$ are always sufficient to generate the symmetric field in $x$ and $y$, provided that $a,b,c$ are distinct positive integers such that $(a,b,c)=1$. In the present paper we prove that in case of prime characteristic $p$ the result still holds, if we assume additionally that $a,b,c,a-b,a-c,b-c$ are prime with $p$. We also provide a counterexample in the case where one of the hypotheses is missing.\n  The result fol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3192","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"}