{"paper":{"title":"Birch's theorem in function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Siu-lun Alan Lee","submitted_at":"2011-09-22T20:31:53Z","abstract_excerpt":"We establish an aysmptotic formula for the number of points with coordinates in $\\mb{F}_q[t]$ on a complete intersection of degree $d$ defined over $\\mb{F}_q[t]$, with explicit error term, provided that the characteristic of $\\mb{F}_q$ is greater than $d$, the codimension of the singular locus of the complete intersection is large enough, and this intersection has a non-singular point at each place of $\\mb{F}_q[t]$. In particular, when this complete intersection is non-singular, we show that it satisfies weak approximation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4953","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"}