{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MHHVAWQ7PQBWABP3UQKY4BFIXP","short_pith_number":"pith:MHHVAWQ7","schema_version":"1.0","canonical_sha256":"61cf505a1f7c036005fba4158e04a8bbc194da43d337d5ff94da463dbb5195e3","source":{"kind":"arxiv","id":"1212.0660","version":2},"attestation_state":"computed","paper":{"title":"On some mean square estimates for the zeta-function in short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2012-12-04T10:05:19Z","abstract_excerpt":"Let $\\Delta(x)$ denote the error term in the Dirichlet divisor problem, and $E(T)$ the error term in the asymptotic formula for the mean square of $|\\zeta(1/2+it)|$. If $E^*(t) = E(t) - 2\\pi\\Delta^*(t/2\\pi)$ with $\\Delta^*(x) =\n  -\\Delta(x) + 2\\Delta(2x) - 1/2\\Delta(4x)$ and we set $\\int_0^T E^*(t)\\,dt = 3\\pi T/4 + R(T)$, then we obtain $$ \\int_T^{T+H}(E^*(t))^2\\,dt \\gg HT^{1/3}\\log^3T $$ and $$ HT\\log^3T \\ll \\int_T^{T+H}R^2(t)\\,dt \\ll HT\\log^3T, $$ for $T^{2/3+\\epsilon}\\le H \\le T$."},"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":"1212.0660","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-04T10:05:19Z","cross_cats_sorted":[],"title_canon_sha256":"99e04dc769a9ec65e211f94dd4989e74e529c4318bb83943f98302a48c5dd6ff","abstract_canon_sha256":"b90f32b24824dcf9220bcdc52bea2b6e60ad900018768c1fa05ef0ab0c8f6ee8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:50.672849Z","signature_b64":"85ns515yu48aJ9lUjuUQLTTUiTlIXOspFOFCMJ/4e6+sDxBMJ79QrvMRPTAYYjJzqcB4ME9i4S4+7itnzakECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61cf505a1f7c036005fba4158e04a8bbc194da43d337d5ff94da463dbb5195e3","last_reissued_at":"2026-05-18T03:09:50.672079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:50.672079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some mean square estimates for the zeta-function in short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2012-12-04T10:05:19Z","abstract_excerpt":"Let $\\Delta(x)$ denote the error term in the Dirichlet divisor problem, and $E(T)$ the error term in the asymptotic formula for the mean square of $|\\zeta(1/2+it)|$. If $E^*(t) = E(t) - 2\\pi\\Delta^*(t/2\\pi)$ with $\\Delta^*(x) =\n  -\\Delta(x) + 2\\Delta(2x) - 1/2\\Delta(4x)$ and we set $\\int_0^T E^*(t)\\,dt = 3\\pi T/4 + R(T)$, then we obtain $$ \\int_T^{T+H}(E^*(t))^2\\,dt \\gg HT^{1/3}\\log^3T $$ and $$ HT\\log^3T \\ll \\int_T^{T+H}R^2(t)\\,dt \\ll HT\\log^3T, $$ for $T^{2/3+\\epsilon}\\le H \\le T$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0660","kind":"arxiv","version":2},"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":"1212.0660","created_at":"2026-05-18T03:09:50.672200+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0660v2","created_at":"2026-05-18T03:09:50.672200+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0660","created_at":"2026-05-18T03:09:50.672200+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHHVAWQ7PQBW","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHHVAWQ7PQBWABP3","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHHVAWQ7","created_at":"2026-05-18T12:27:14.488303+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/MHHVAWQ7PQBWABP3UQKY4BFIXP","json":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP.json","graph_json":"https://pith.science/api/pith-number/MHHVAWQ7PQBWABP3UQKY4BFIXP/graph.json","events_json":"https://pith.science/api/pith-number/MHHVAWQ7PQBWABP3UQKY4BFIXP/events.json","paper":"https://pith.science/paper/MHHVAWQ7"},"agent_actions":{"view_html":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP","download_json":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP.json","view_paper":"https://pith.science/paper/MHHVAWQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0660&json=true","fetch_graph":"https://pith.science/api/pith-number/MHHVAWQ7PQBWABP3UQKY4BFIXP/graph.json","fetch_events":"https://pith.science/api/pith-number/MHHVAWQ7PQBWABP3UQKY4BFIXP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP/action/storage_attestation","attest_author":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP/action/author_attestation","sign_citation":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP/action/citation_signature","submit_replication":"https://pith.science/pith/MHHVAWQ7PQBWABP3UQKY4BFIXP/action/replication_record"}},"created_at":"2026-05-18T03:09:50.672200+00:00","updated_at":"2026-05-18T03:09:50.672200+00:00"}