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Araujo","submitted_at":"2013-12-27T16:45:19Z","abstract_excerpt":"In this paper, we consider $D=\\mathbb{Z}[\\theta]$, where\n  $$\\theta= \\sqrt{-k} \\,\\,\\,\\, \\mbox{if}\\;\\;\\;-k\\not\\equiv 1 \\;(\\mbox{mod}\\;4)\\,\\,\\,\\,\\mbox{or}\\,\\,\\,\\, \\theta=\\frac{\\sqrt{-k}+1}{2} \\,\\,\\,\\, \\mbox{if}\\;\\;\\;-k\\equiv 1 \\;(\\mbox{mod}\\;4),$$\n  $k\\geq 2$ is a squarefree integer, and we proved that the number $R(y)$ of representations of a monic polynomial $f(x)\\in \\mathbb{Z}[\\theta][x]$, of degree $d\\geq 1$, as a sum of two monic irreducible polynomials $g(x)$ and $h(x)$ in $\\mathbb{Z}[\\theta][x]$, with the coefficients of $g(x)$ and $h(x)$ bounded in complex modulus by $y$, is asymptotic t"},"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":"1312.7295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-27T16:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"d9a00dd8e30b8edba3be0f656fd7497bded4a5e026298296d3a8e8d15b40101d","abstract_canon_sha256":"47463d41154544d77db33cc58a801ac7a40aaafeb5cea6eb3cd64b2a332a6a8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:11.644839Z","signature_b64":"tEE17JiErZNflqEpxUWRMjHPpsOEz5FptAt4n0txNBwfnt0ZN3EAOySti54GKEbSgEa0fjDwvHO+KvXhUlkhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17d20055407d09db1f7f10cb61c9d64938df1e16cc2a73f288df50b81603a364","last_reissued_at":"2026-05-18T02:12:11.644175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:11.644175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An asymptotic formula for Goldbach's conjecture with monic polynomials in $\\mathbb{Z}[\\theta][x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ab\\'ilio Lemos, Anderson L. 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Araujo","submitted_at":"2013-12-27T16:45:19Z","abstract_excerpt":"In this paper, we consider $D=\\mathbb{Z}[\\theta]$, where\n  $$\\theta= \\sqrt{-k} \\,\\,\\,\\, \\mbox{if}\\;\\;\\;-k\\not\\equiv 1 \\;(\\mbox{mod}\\;4)\\,\\,\\,\\,\\mbox{or}\\,\\,\\,\\, \\theta=\\frac{\\sqrt{-k}+1}{2} \\,\\,\\,\\, \\mbox{if}\\;\\;\\;-k\\equiv 1 \\;(\\mbox{mod}\\;4),$$\n  $k\\geq 2$ is a squarefree integer, and we proved that the number $R(y)$ of representations of a monic polynomial $f(x)\\in \\mathbb{Z}[\\theta][x]$, of degree $d\\geq 1$, as a sum of two monic irreducible polynomials $g(x)$ and $h(x)$ in $\\mathbb{Z}[\\theta][x]$, with the coefficients of $g(x)$ and $h(x)$ bounded in complex modulus by $y$, is asymptotic t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7295","kind":"arxiv","version":2},"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":"1312.7295","created_at":"2026-05-18T02:12:11.644276+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.7295v2","created_at":"2026-05-18T02:12:11.644276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7295","created_at":"2026-05-18T02:12:11.644276+00:00"},{"alias_kind":"pith_short_12","alias_value":"C7JAAVKAPUE5","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"C7JAAVKAPUE5WH37","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"C7JAAVKA","created_at":"2026-05-18T12:27:40.988391+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/C7JAAVKAPUE5WH37CDFWDSOWJE","json":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE.json","graph_json":"https://pith.science/api/pith-number/C7JAAVKAPUE5WH37CDFWDSOWJE/graph.json","events_json":"https://pith.science/api/pith-number/C7JAAVKAPUE5WH37CDFWDSOWJE/events.json","paper":"https://pith.science/paper/C7JAAVKA"},"agent_actions":{"view_html":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE","download_json":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE.json","view_paper":"https://pith.science/paper/C7JAAVKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.7295&json=true","fetch_graph":"https://pith.science/api/pith-number/C7JAAVKAPUE5WH37CDFWDSOWJE/graph.json","fetch_events":"https://pith.science/api/pith-number/C7JAAVKAPUE5WH37CDFWDSOWJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE/action/storage_attestation","attest_author":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE/action/author_attestation","sign_citation":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE/action/citation_signature","submit_replication":"https://pith.science/pith/C7JAAVKAPUE5WH37CDFWDSOWJE/action/replication_record"}},"created_at":"2026-05-18T02:12:11.644276+00:00","updated_at":"2026-05-18T02:12:11.644276+00:00"}