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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.04286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-12T07:37:33Z","cross_cats_sorted":[],"title_canon_sha256":"d44cba4c53f24a5f78501b39cffd4eacfb7f51622cf7278cbe1d6d6811f9880f","abstract_canon_sha256":"8f301f3c15052578fc1c36263657a94acab3bf4fb5bd6fb1f52cce7fb71a2d3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:52.858326Z","signature_b64":"wlwQcKbruFSVqgrOcQ2f6+yL93lw4WjzrBn3OP54Jv3jcPaBjwOGdELfY9lnvbQ0xjsAtExHjKLJR1krsotWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a91032cefbf6ea30f26aa38e053e9b4bcd6bb0ca42a0f5b1147beff50ee76d18","last_reissued_at":"2026-05-18T00:05:52.857724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:52.857724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\eta$. 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