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Our estimate asserts that \\mathcal{V}(d,s,\\bfs{a})=\\mu_d\\,q+\\mathcal{O}(q^{1/2}), where \\mathcal{V}(d,s,\\bfs{a}) is such an average cardinality, \\mu_d:=\\sum_{r=1}^d{(-1)^{r-1}}/{r!} and \\bfs{a}:=(a_{d-1},...,a_{d-s}). We also prove that \\mathcal{V}_2(d,s,\\bfs{a})=\\mu_d^2\\,q^2+\\mathcal{O}(q^{3/2}), where that \\mathcal{V}_2(d,s,\\bfs{a}) is the average second moment on any family of monic polynomials of Fq[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":"1310.3293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-11T21:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"7bb6db156faf44ada8b806efaecd2c7f62a1de17c400e97fb529cc54b6c93480","abstract_canon_sha256":"37af1fa8d9765f34cda10df92cd9f65530c3d3f19f052ba37e9a5e56d7a851d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:36.213916Z","signature_b64":"Q8haExYyKfs313vxWYzvZhlA5TkzQ1cfU9JH9mZWp+YGCM88dhzqYRgLKZvHS8MkpjU3JHROVdTpoP2BIwHUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c01cd2f9af924235d7384a9762ab97c589da438a924fbb4d5ea7a03360c232e9","last_reissued_at":"2026-05-18T03:10:36.213455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:36.213455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the value set of small families of polynomials over a finite field, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Guillermo Matera, Mariana P\\'erez, Melina Privitelli","submitted_at":"2013-10-11T21:04:58Z","abstract_excerpt":"We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients a_{d-1},...,a_{d-s} are fixed. Our estimate asserts that \\mathcal{V}(d,s,\\bfs{a})=\\mu_d\\,q+\\mathcal{O}(q^{1/2}), where \\mathcal{V}(d,s,\\bfs{a}) is such an average cardinality, \\mu_d:=\\sum_{r=1}^d{(-1)^{r-1}}/{r!} and \\bfs{a}:=(a_{d-1},...,a_{d-s}). We also prove that \\mathcal{V}_2(d,s,\\bfs{a})=\\mu_d^2\\,q^2+\\mathcal{O}(q^{3/2}), where that \\mathcal{V}_2(d,s,\\bfs{a}) is the average second moment on any family of monic polynomials of Fq[T] "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3293","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":"1310.3293","created_at":"2026-05-18T03:10:36.213524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.3293v1","created_at":"2026-05-18T03:10:36.213524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3293","created_at":"2026-05-18T03:10:36.213524+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAONF6NPSJBD","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAONF6NPSJBDLVZY","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAONF6NP","created_at":"2026-05-18T12:28:06.772260+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/YAONF6NPSJBDLVZYJKLWFK4XYW","json":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW.json","graph_json":"https://pith.science/api/pith-number/YAONF6NPSJBDLVZYJKLWFK4XYW/graph.json","events_json":"https://pith.science/api/pith-number/YAONF6NPSJBDLVZYJKLWFK4XYW/events.json","paper":"https://pith.science/paper/YAONF6NP"},"agent_actions":{"view_html":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW","download_json":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW.json","view_paper":"https://pith.science/paper/YAONF6NP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.3293&json=true","fetch_graph":"https://pith.science/api/pith-number/YAONF6NPSJBDLVZYJKLWFK4XYW/graph.json","fetch_events":"https://pith.science/api/pith-number/YAONF6NPSJBDLVZYJKLWFK4XYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW/action/storage_attestation","attest_author":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW/action/author_attestation","sign_citation":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW/action/citation_signature","submit_replication":"https://pith.science/pith/YAONF6NPSJBDLVZYJKLWFK4XYW/action/replication_record"}},"created_at":"2026-05-18T03:10:36.213524+00:00","updated_at":"2026-05-18T03:10:36.213524+00:00"}