{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:MGEWHMMJDS4JZLERWSBAR2SF7R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d8d405e5cf15c6302d85797b75776224e8f407caf1de68bea0656b5a147caecb","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2007-06-14T13:02:04Z","title_canon_sha256":"c6b0ce644fc8a5220e79d228f6a8f132f6fe2e0827b749f53bd81f0c335b9ee7"},"schema_version":"1.0","source":{"id":"0706.2112","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.2112","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"0706.2112v5","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.2112","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"MGEWHMMJDS4J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"MGEWHMMJDS4JZLER","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"MGEWHMMJ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:313ab3009ebbcd110942baa7a1519c75f25fb4afe71522e5881d683795fe85d0","target":"graph","created_at":"2026-05-18T02:16:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\F_q$ ($q=p^r$) be a finite field. In this paper the number of irreducible polynomials of degree $m$ in $\\F_q[x]$ with prescribed trace and norm coefficients is calculated in certain special cases and a general bound for that number is obtained improving the bound by Wan if $m$ is small compared to $q$. As a corollary, sharp bounds are obtained for the number of elements in $\\F_{q^3}$ with prescribed trace and norm over $\\F_q$ improving the estimates by Katz in this special case. Moreover, a characterization of Kloosterman sums over $\\F_{2^r}$ divisible by three is given generalizing the ","authors_text":"Marko Moisio","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-06-14T13:02:04Z","title":"Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2112","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dffb413d0b3a9ac0645e0c92c0da41ee6d04686a0d0f69c79c2d807fe04e8248","target":"record","created_at":"2026-05-18T02:16:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d8d405e5cf15c6302d85797b75776224e8f407caf1de68bea0656b5a147caecb","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2007-06-14T13:02:04Z","title_canon_sha256":"c6b0ce644fc8a5220e79d228f6a8f132f6fe2e0827b749f53bd81f0c335b9ee7"},"schema_version":"1.0","source":{"id":"0706.2112","kind":"arxiv","version":5}},"canonical_sha256":"618963b1891cb89cac91b48208ea45fc620b6b8abedb5504ba235cab5ecd83a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"618963b1891cb89cac91b48208ea45fc620b6b8abedb5504ba235cab5ecd83a0","first_computed_at":"2026-05-18T02:16:30.126963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:30.126963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8biub1jUykKxQnduDpsS3oe1uuvUi0+ka4vs74ZyrTC6+GytNSVoaED6jJ9fymxzVKCLnYm/cGaK8Q66brJeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:30.127557Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.2112","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dffb413d0b3a9ac0645e0c92c0da41ee6d04686a0d0f69c79c2d807fe04e8248","sha256:313ab3009ebbcd110942baa7a1519c75f25fb4afe71522e5881d683795fe85d0"],"state_sha256":"3f210a5e4ab09a2fcb01116b81bcb74de9abc53a755a7a713c020e3f27de32a8"}