{"paper":{"title":"On Global $\\mathcal P$-Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Xiang-dong Hou","submitted_at":"2014-05-19T17:49:45Z","abstract_excerpt":"Let $\\Bbb F_q$ be a finite field with $\\text{char}\\,\\Bbb F_q=p$ and $n>0$ an integer with $\\text{gcd}(n, \\log_pq)=1$. Let $(\\ )^*:\\Bbb F_q({\\tt x}_0,\\dots,{\\tt x}_{n-1})\\to\\Bbb F_q({\\tt x}_0,\\dots,{\\tt x}_{n-1})$ be the $\\Bbb F_q$-monomorphism defined by ${\\tt x}_i^*={\\tt x}_{i+1}$ for $0\\le i< n-1$ and ${\\tt x}_{n-1}^*={\\tt x}_0^q$. For $f,g\\in\\Bbb F_q({\\tt x}_0,\\dots,{\\tt x}_{n-1})\\setminus\\Bbb F_q$, define $f\\circ g=f(g,g^*,\\dots,g^{(n-1)*})$. Then $(\\Bbb F_q({\\tt x}_0,\\dots,{\\tt x}_{n-1})\\setminus\\Bbb F_q,\\,\\circ)$ is a monoid whose invertible elements are called global $\\mathcal P$-forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4816","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"}