{"paper":{"title":"Contributions to a conjecture of Mueller and Schmidt on Thue inequalities","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Divyum Sharma, N. Saradha","submitted_at":"2016-03-22T15:50:31Z","abstract_excerpt":"Let $F(X,Y)=\\sum\\limits_{i=0}^sa_iX^{r_i}Y^{r-r_i}\\in\\mathbb{Z}[X,Y]$ be a form of degree $r=r_s\\geq 3$, irreducible over $\\mathbb{Q}$ and having at most $s+1$ non-zero coefficients. Mueller and Schmidt showed that the number of solutions of the Thue inequality \\[\n  |F(X,Y)|\\leq h \\] is $\\ll s^2h^{2/r}(1+\\log h^{1/r})$. They $\\textit{conjectured}$ that $s^2$ may be replaced by $s$. Let \\[\n  \\Psi = \\max_{0\\leq i\\leq s} \\max\\left( \\sum_{w=0}^{i-1}\\frac{1}{r_i-r_w},\\sum_{w= i+1}^{s}\\frac{1}{r_w-r_i}\\right). \\]\n  Then we show that $s^2$ may be replaced by $\\max(s\\log^3s, se^{\\Psi})$. We also show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06837","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"}