{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WGPHLPO6STWNMZZFEF6NMK5OHU","short_pith_number":"pith:WGPHLPO6","schema_version":"1.0","canonical_sha256":"b19e75bdde94ecd66725217cd62bae3d285b46f29c4f9949703f863639ed363e","source":{"kind":"arxiv","id":"1607.03064","version":1},"attestation_state":"computed","paper":{"title":"Computing relative power integral bases in a family of quartic extensions of imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Borka Jadrijevi\\'c, Zrinka Franu\\v{s}i\\'c","submitted_at":"2016-07-11T18:11:56Z","abstract_excerpt":"Let $M$ be an imaginary quadratic field with the ring of integers $\\mathbb{Z}_{M}$ and let $\\xi$ be a root of polynomial $$f\\left( x\\right) =x^{4}-2cx^{3}+2x^{2}+2cx+1,$$ where $c\\in\\mathbb{Z}_{M},$ $c\\notin\\left\\{ 0,\\pm2\\right\\}$. We consider an infinite family of octic fields $K_{c}=M\\left( \\xi\\right)$ with the ring of integers $\\mathbb{Z}_{K_{c}}.$ Our goal is to determine all generators of relative power integral basis of $\\mathcal{O=}\\mathbb{Z}_{M}\\left[ \\xi\\right]$ over $\\mathbb{Z}_{M}.$ We show that our problem reduces to solving the system of relative Pellian equations \\[ cV^{2}-\\left("},"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":"1607.03064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-11T18:11:56Z","cross_cats_sorted":[],"title_canon_sha256":"3d67e3cc59ef419bec1cc31768da2678a7e2e8a3c322de2f536bdc60fa705c94","abstract_canon_sha256":"b89bc84dc252c3618dc5666e3902ee7f1670809fc7760da804b2ae9bf5722055"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:14.062587Z","signature_b64":"Nn/03UWXIhpnl49v3HUaSvjrX/1zIGWS3xVieUIE2aJIHdXKjt9MTHHZVKM+P7lWU/pM033hUccsJmQeKQw3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b19e75bdde94ecd66725217cd62bae3d285b46f29c4f9949703f863639ed363e","last_reissued_at":"2026-05-18T01:11:14.062166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:14.062166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing relative power integral bases in a family of quartic extensions of imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Borka Jadrijevi\\'c, Zrinka Franu\\v{s}i\\'c","submitted_at":"2016-07-11T18:11:56Z","abstract_excerpt":"Let $M$ be an imaginary quadratic field with the ring of integers $\\mathbb{Z}_{M}$ and let $\\xi$ be a root of polynomial $$f\\left( x\\right) =x^{4}-2cx^{3}+2x^{2}+2cx+1,$$ where $c\\in\\mathbb{Z}_{M},$ $c\\notin\\left\\{ 0,\\pm2\\right\\}$. We consider an infinite family of octic fields $K_{c}=M\\left( \\xi\\right)$ with the ring of integers $\\mathbb{Z}_{K_{c}}.$ Our goal is to determine all generators of relative power integral basis of $\\mathcal{O=}\\mathbb{Z}_{M}\\left[ \\xi\\right]$ over $\\mathbb{Z}_{M}.$ We show that our problem reduces to solving the system of relative Pellian equations \\[ cV^{2}-\\left("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03064","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":"1607.03064","created_at":"2026-05-18T01:11:14.062232+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.03064v1","created_at":"2026-05-18T01:11:14.062232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03064","created_at":"2026-05-18T01:11:14.062232+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGPHLPO6STWN","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGPHLPO6STWNMZZF","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGPHLPO6","created_at":"2026-05-18T12:30:48.956258+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/WGPHLPO6STWNMZZFEF6NMK5OHU","json":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU.json","graph_json":"https://pith.science/api/pith-number/WGPHLPO6STWNMZZFEF6NMK5OHU/graph.json","events_json":"https://pith.science/api/pith-number/WGPHLPO6STWNMZZFEF6NMK5OHU/events.json","paper":"https://pith.science/paper/WGPHLPO6"},"agent_actions":{"view_html":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU","download_json":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU.json","view_paper":"https://pith.science/paper/WGPHLPO6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.03064&json=true","fetch_graph":"https://pith.science/api/pith-number/WGPHLPO6STWNMZZFEF6NMK5OHU/graph.json","fetch_events":"https://pith.science/api/pith-number/WGPHLPO6STWNMZZFEF6NMK5OHU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU/action/storage_attestation","attest_author":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU/action/author_attestation","sign_citation":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU/action/citation_signature","submit_replication":"https://pith.science/pith/WGPHLPO6STWNMZZFEF6NMK5OHU/action/replication_record"}},"created_at":"2026-05-18T01:11:14.062232+00:00","updated_at":"2026-05-18T01:11:14.062232+00:00"}