{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FKHNW2ZV3AVJ2TTOIXHUTQYOKJ","short_pith_number":"pith:FKHNW2ZV","schema_version":"1.0","canonical_sha256":"2a8edb6b35d82a9d4e6e45cf49c30e52404a88490e55a00f6f045e946b7be5fb","source":{"kind":"arxiv","id":"1603.06837","version":1},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.06837","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2016-03-22T15:50:31Z","cross_cats_sorted":[],"title_canon_sha256":"3428f6fec18bb7a0fe0184994c57b00c2e9f4690512b6ffbbfbca581c57e6ecb","abstract_canon_sha256":"e186d48fc6dc823c5e5f29f3da69785c29d90fa1973016bddaca140c729843c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:34.604160Z","signature_b64":"vR/7jU7gIWR1XjC1nLPIW1+lAp2V4zLLD3PBM8smks5rDp/FzoULblxUj/HNC1HZhw+HiirzcF8TtkI3rtZ7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a8edb6b35d82a9d4e6e45cf49c30e52404a88490e55a00f6f045e946b7be5fb","last_reissued_at":"2026-05-18T01:18:34.603689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:34.603689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.06837","created_at":"2026-05-18T01:18:34.603765+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.06837v1","created_at":"2026-05-18T01:18:34.603765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06837","created_at":"2026-05-18T01:18:34.603765+00:00"},{"alias_kind":"pith_short_12","alias_value":"FKHNW2ZV3AVJ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FKHNW2ZV3AVJ2TTO","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FKHNW2ZV","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ","json":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ.json","graph_json":"https://pith.science/api/pith-number/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/graph.json","events_json":"https://pith.science/api/pith-number/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/events.json","paper":"https://pith.science/paper/FKHNW2ZV"},"agent_actions":{"view_html":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ","download_json":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ.json","view_paper":"https://pith.science/paper/FKHNW2ZV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.06837&json=true","fetch_graph":"https://pith.science/api/pith-number/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/action/storage_attestation","attest_author":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/action/author_attestation","sign_citation":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/action/citation_signature","submit_replication":"https://pith.science/pith/FKHNW2ZV3AVJ2TTOIXHUTQYOKJ/action/replication_record"}},"created_at":"2026-05-18T01:18:34.603765+00:00","updated_at":"2026-05-18T01:18:34.603765+00:00"}