{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JNQ3S3ZDIR6JZHKCTISVTFSMMF","short_pith_number":"pith:JNQ3S3ZD","schema_version":"1.0","canonical_sha256":"4b61b96f23447c9c9d429a2559964c614091621fe8ef24f02409d61f8ba672c6","source":{"kind":"arxiv","id":"1711.05358","version":4},"attestation_state":"computed","paper":{"title":"Linear and quadratic uniformity of the M\\\"obius function over $\\mathbb{F}_q[t]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Pierre-Yves Bienvenu, Th\\'ai Ho\\`ang L\\^e","submitted_at":"2017-11-14T23:43:05Z","abstract_excerpt":"We examine correlations of the M\\\"obius function over $\\mathbb{F}_q[t]$ with linear or quadratic phases, that is, averages of the form \\begin{equation} \\label{eq:average} \\frac{1}{q^n}\\sum_{\\text{deg }f<n} \\mu(f)\\chi(Q(f)) \\end{equation} for an additive character $\\chi$ over $\\mathbb{F}_q$ and a polynomial $Q\\in\\mathbb{F}_q[x_0,\\ldots,x_{n-1}]$ of degree at most 2 in the coefficients $x_0,\\ldots, x_{n-1}$ of $f=\\sum_{i< n}x_i t^i$. Like in the integers, it is reasonable to expect that, due to the random-like behaviour of $\\mu$, such sums should exhibit considerable cancellation. In this paper "},"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":"1711.05358","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-14T23:43:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3f933e772d170e4aa64e911b49e723cd92b127fa3b8962716d1703a21d15542a","abstract_canon_sha256":"eb161d9e05395fbf4dc3c4c7da78603ca17a5b9da287646cacbf63295bad54d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:34.178782Z","signature_b64":"9FhSwtsDSKmC5+H6c2g3jV5WRoTssRMvV3+54/xYwlPitv/G29HOPqhN6DI67CAdcGMmeRxocG0X+kR/tz9mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b61b96f23447c9c9d429a2559964c614091621fe8ef24f02409d61f8ba672c6","last_reissued_at":"2026-05-18T00:04:34.178012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:34.178012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear and quadratic uniformity of the M\\\"obius function over $\\mathbb{F}_q[t]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Pierre-Yves Bienvenu, Th\\'ai Ho\\`ang L\\^e","submitted_at":"2017-11-14T23:43:05Z","abstract_excerpt":"We examine correlations of the M\\\"obius function over $\\mathbb{F}_q[t]$ with linear or quadratic phases, that is, averages of the form \\begin{equation} \\label{eq:average} \\frac{1}{q^n}\\sum_{\\text{deg }f<n} \\mu(f)\\chi(Q(f)) \\end{equation} for an additive character $\\chi$ over $\\mathbb{F}_q$ and a polynomial $Q\\in\\mathbb{F}_q[x_0,\\ldots,x_{n-1}]$ of degree at most 2 in the coefficients $x_0,\\ldots, x_{n-1}$ of $f=\\sum_{i< n}x_i t^i$. Like in the integers, it is reasonable to expect that, due to the random-like behaviour of $\\mu$, such sums should exhibit considerable cancellation. In this paper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05358","kind":"arxiv","version":4},"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":"1711.05358","created_at":"2026-05-18T00:04:34.178139+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05358v4","created_at":"2026-05-18T00:04:34.178139+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05358","created_at":"2026-05-18T00:04:34.178139+00:00"},{"alias_kind":"pith_short_12","alias_value":"JNQ3S3ZDIR6J","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JNQ3S3ZDIR6JZHKC","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JNQ3S3ZD","created_at":"2026-05-18T12:31:24.725408+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/JNQ3S3ZDIR6JZHKCTISVTFSMMF","json":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF.json","graph_json":"https://pith.science/api/pith-number/JNQ3S3ZDIR6JZHKCTISVTFSMMF/graph.json","events_json":"https://pith.science/api/pith-number/JNQ3S3ZDIR6JZHKCTISVTFSMMF/events.json","paper":"https://pith.science/paper/JNQ3S3ZD"},"agent_actions":{"view_html":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF","download_json":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF.json","view_paper":"https://pith.science/paper/JNQ3S3ZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05358&json=true","fetch_graph":"https://pith.science/api/pith-number/JNQ3S3ZDIR6JZHKCTISVTFSMMF/graph.json","fetch_events":"https://pith.science/api/pith-number/JNQ3S3ZDIR6JZHKCTISVTFSMMF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/action/storage_attestation","attest_author":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/action/author_attestation","sign_citation":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/action/citation_signature","submit_replication":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/action/replication_record"}},"created_at":"2026-05-18T00:04:34.178139+00:00","updated_at":"2026-05-18T00:04:34.178139+00:00"}