{"paper":{"title":"Evaluating Prime Power Gauss and Jacobi Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Pinner, Misty Long, Vincent Pigno","submitted_at":"2014-10-22T20:23:19Z","abstract_excerpt":"We show that for any mod $p^m$ characters, $\\chi_1, \\dots, \\chi_k,$ the Jacobi sum, $$ \\sum_{x_1=1}^{p^m}\\dots \\sum_{\\substack{x_k=1\\\\x_1+\\dots+x_k=B}}^{p^m}\\chi_1(x_1)\\dots \\chi_k(x_k), $$ has a simple evaluation when $m$ is sufficiently large (for $m\\geq 2$ if $p\\nmid B$). As part of the proof we give a simple evaluation of the mod $p^m$ Gauss sums when $m\\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6179","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"}