{"paper":{"title":"Estimates for Character Sums with Various Convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brandon Hanson","submitted_at":"2015-09-14T23:55:23Z","abstract_excerpt":"We provide estimates for sums of the form \\[\\left|\\sum_{a\\in A}\\sum_{b\\in B}\\sum_{c\\in C}\\chi(a+b+c)\\right|\\] and \\[\\left|\\sum_{a\\in A}\\sum_{b\\in B}\\sum_{c\\in C}\\sum_{d\\in D}\\chi(a+b+cd)\\right|\\] when $A,B,C,D\\subset \\mathbb F_p$, the field with $p$ elements and $\\chi$ is a non-trivial multiplicative character modulo $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04354","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"}