{"paper":{"title":"On the Bound of Inverse Images of a Polynomial Map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Ilya Vyugin","submitted_at":"2018-11-21T20:12:29Z","abstract_excerpt":"Let $f_1(x),\\ldots,f_n(x)$ be some polynomials. The upper bound on the number of $x\\in\\mathbb F_p$ such that $f_1(x),\\ldots,f_n(x)$ are roots of unit of order $t$ is obtained. This bound generalize the bound of the paper \\cite{V-S} to the case of polynomials of degrees greater than one. The bound is obtained over fields of positive characteristic and over the complex field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08930","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"}