{"paper":{"title":"Binomial Character Sums Modulo Prime Powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Pinner, Vincent Pigno","submitted_at":"2014-10-23T20:26:12Z","abstract_excerpt":"We show that the binomial and related multiplicative character sums $$ \\sum_{\\stackrel{x=1}{(x,p)=1}}^{p^m} \\chi (x^l(Ax^k +B)^w),\\hspace{3ex} \\sum_{x=1}^{p^m} \\chi_1 (x)\\chi_2(Ax^k +B), $$ have a simple evaluation for large enough $m$ (for $m\\geq 2$ if $p\\nmid ABk$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6494","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"}