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For distinct polynomials a_1, ..., a_r over F_q of degree <n let \\pi(q,n;a) be the number of monic polynomials f over F_q of degree n such that f+a_1, ..., f+a_r are simultaneously irreducible. We prove that \\pi(q,n;a) asymptotically equals q^n/n^r as q tends to infinity on odd prime powers and n,r are fixed (the tuple a1,...,a_r need not be fixed)."},"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":"1206.3930","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-18T13:44:08Z","cross_cats_sorted":[],"title_canon_sha256":"00dfea63ddca1627d744fd061f25d10a053086f583c7329c9d0a773880680057","abstract_canon_sha256":"6ddd74c1a9c2b495195779d1fc2fbc6459c899c664d5f2db187cdac4f57523e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:04.361373Z","signature_b64":"2aePVk99mWvyE4UF31uVEYP93fZl9rKAd88nJhgRZafrdbZTCPHxj82/6cfTHdpZuxf/nNTyGFnC04ScudwuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f51ee91ac6e9cce54d3c4f6a87c93a426ef395da38521ab20cb46d43d766c9d","last_reissued_at":"2026-05-18T03:44:04.360608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:04.360608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hardy-Littlewood tuple conjecture over large finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lior Bary-Soroker","submitted_at":"2012-06-18T13:44:08Z","abstract_excerpt":"We prove the following function field analog of the Hardy-Littlewood conjecture (which generalizes the twin prime conjecture) over large finite fields. Let n,r be positive integers and q an odd prime power. For distinct polynomials a_1, ..., a_r over F_q of degree <n let \\pi(q,n;a) be the number of monic polynomials f over F_q of degree n such that f+a_1, ..., f+a_r are simultaneously irreducible. We prove that \\pi(q,n;a) asymptotically equals q^n/n^r as q tends to infinity on odd prime powers and n,r are fixed (the tuple a1,...,a_r need not be fixed)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3930","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.3930","created_at":"2026-05-18T03:44:04.360726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.3930v3","created_at":"2026-05-18T03:44:04.360726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3930","created_at":"2026-05-18T03:44:04.360726+00:00"},{"alias_kind":"pith_short_12","alias_value":"D5I65ENMN2OM","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"D5I65ENMN2OM4VGT","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"D5I65ENM","created_at":"2026-05-18T12:27:01.376967+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/D5I65ENMN2OM4VGTYT3KQ7ETUQ","json":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ.json","graph_json":"https://pith.science/api/pith-number/D5I65ENMN2OM4VGTYT3KQ7ETUQ/graph.json","events_json":"https://pith.science/api/pith-number/D5I65ENMN2OM4VGTYT3KQ7ETUQ/events.json","paper":"https://pith.science/paper/D5I65ENM"},"agent_actions":{"view_html":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ","download_json":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ.json","view_paper":"https://pith.science/paper/D5I65ENM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.3930&json=true","fetch_graph":"https://pith.science/api/pith-number/D5I65ENMN2OM4VGTYT3KQ7ETUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/D5I65ENMN2OM4VGTYT3KQ7ETUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ/action/storage_attestation","attest_author":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ/action/author_attestation","sign_citation":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ/action/citation_signature","submit_replication":"https://pith.science/pith/D5I65ENMN2OM4VGTYT3KQ7ETUQ/action/replication_record"}},"created_at":"2026-05-18T03:44:04.360726+00:00","updated_at":"2026-05-18T03:44:04.360726+00:00"}