{"paper":{"title":"Representation of Small Integers by Binary Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shabnam Akhtari","submitted_at":"2015-08-14T18:47:41Z","abstract_excerpt":"We establish some upper bounds for the number of integer solutions to the Thue inequality $|F(x , y)| \\leq m$, where $F$ is a binary form of degree $n \\geq 3$ and with non-zero discriminant $D$, and $m$ is an integer. Our upper bounds are independent of $m$, when $m$ is smaller than $|D|^{\\frac{1}{4(n-1)}}$. We also consider the Thue equation $|F(x , y)| = m$ and give some upper bounds for the number of its integral solutions. In the case of equation, our upper bounds will be independent of integer $m$, when $ m < |D|^{\\frac{1}{2(n-1)}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03602","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"}