{"paper":{"title":"Thue's inequalities and the hypergeometric method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Divyum Sharma, N. Saradha, Shabnam Akhtari","submitted_at":"2016-03-10T17:27:53Z","abstract_excerpt":"Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape $0<|F(x, y)| \\leq h$, where $F(x , y) =(\\alpha x + \\beta y)^r -(\\gamma x + \\delta y)^r \\in \\mathbb{Z}[x ,y]$, $\\alpha$, $\\beta$, $\\gamma$ and $\\delta$ are algebraic constants with $\\alpha\\delta-\\beta\\gamma \\neq 0$, and $r \\geq 3$ and $h$ are integers. As an important application, we pay special attention to the binomial Thue's inequaities $|ax^r - by^r| \\leq c$. The proofs are based on the hypergeometric method of Thue and Siegel and its refinement b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03340","kind":"arxiv","version":3},"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"}