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We obtain an explicit version of the Hooley--Katz estimate $||V(F_{\\hskip-0.7mm q})|-p_r|=\\mathcal{O}(q^{(r+s+1)/2})$, where $|V(F_{\\hskip-0.7mm q})|$ denotes the number of $F_{\\hskip-0.7mm q}$-rational points of $V$ and $p_r:=|\\mathbb{P}^r(F_{\\hskip-0.7mm q})|$. Our estimate improves all the previous estimates in several important cases. Our approach relies on tools of classical algebraic"},"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":"1412.7446","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-23T17:11:06Z","cross_cats_sorted":[],"title_canon_sha256":"38034d47173ab9a096d6bbec5179367f35a0ba37610c81555c5304ed98ed9d9c","abstract_canon_sha256":"e96ea0f633177dd3c1373c203c967e0dcbf6ae2a0df1393c040f0eda53ea235e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:38.882139Z","signature_b64":"uJMccQPD3TU/q80JX2oDl1CaBUieezkvzSA9vI0gSH98XBYgoVephGQG31Kzd0D0O+BSB28z2ByHplfG1+/SAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8516eaf1136cc2029842bad240d9b6ef97860ae579c2a903e9438482cf1a2237","last_reissued_at":"2026-05-18T02:30:38.881697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:38.881697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit Estimates for the Number of Rational Points of Singular Complete Intersections over a Finite Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Guillermo Matera, Mariana P\\'erez, Melina Privitelli","submitted_at":"2014-12-23T17:11:06Z","abstract_excerpt":"Let $V\\subset\\mathbb{P}^n(\\overline{F}_{\\hskip-0.7mm q})$ be a complete intersection defined over a finite field $F_{\\hskip-0.7mm q}$ of dimension $r$ and singular locus of dimension at most $0\\le s\\le r-2$. We obtain an explicit version of the Hooley--Katz estimate $||V(F_{\\hskip-0.7mm q})|-p_r|=\\mathcal{O}(q^{(r+s+1)/2})$, where $|V(F_{\\hskip-0.7mm q})|$ denotes the number of $F_{\\hskip-0.7mm q}$-rational points of $V$ and $p_r:=|\\mathbb{P}^r(F_{\\hskip-0.7mm q})|$. Our estimate improves all the previous estimates in several important cases. 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