{"paper":{"title":"Equidistributions of Jacobi sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ping Xi","submitted_at":"2018-09-12T07:37:33Z","abstract_excerpt":"Let $\\mathbf{F}_q$ be a finite field of $q$ elements. We show that the normalized Jacobi sum $J(\\chi,\\eta)/\\sqrt{q}$, for each fixed non-trivial multiplicative character $\\eta$, becomes equidistributed in the unit circle as $q\\rightarrow+\\infty,$ when $\\chi$ runs over all non-trivial multiplicative characters different from $\\eta^{-1}.$ Previously, the similar equidistribution was obtained by Katz and Zheng by varying both of $\\chi$ and $\\eta$. On the other hand, we also obtain the equidistribution of $J(\\chi,\\eta)$ as $(\\chi,\\eta)$ runs over $\\mathcal{X}\\times\\mathcal{Y}\\subseteq(\\widehat{\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04286","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"}