{"paper":{"title":"A characterization of Jacobi sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Snowden","submitted_at":"2024-11-22T15:35:36Z","abstract_excerpt":"Let $\\mathbb{M}$ be the group of multiplicative characters of a finite field $\\mathbb{F}$, and let $\\mathbb{J}(\\alpha, \\beta)$ be the Jacobi sum, for $\\alpha, \\beta \\in \\mathbb{M}$. We observe that the function $\\mathbb{J} \\colon \\mathbb{M} \\times \\mathbb{M} \\to \\mathbf{C}$ satisfies three elementary properties. We show that these properties (very nearly) characterize Jacobi sums: if $M$ is an arbitrary non-trivial finite abelian group and $J \\colon M \\times M \\to \\mathbf{C}$ is a function satisfying these properties then $M$ is naturally the group of multiplicative characters of a finite fiel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15011","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15011/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}