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This is shown to be true for certain specific values of the natural numbers $k,\\ell,m$, and the explicitly determined range of $G = G(T;k,\\ell,m)$. The application to a mean square bound for the Mellin transform function of $|\\zeta(1/2+ix)|^4$ is given."},"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":"0803.2353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-03-16T14:12:09Z","cross_cats_sorted":[],"title_canon_sha256":"9e3a0dfb3ae9365b04f3673e461317dcf273ea8ae02d4d1e17fe9891a5fd0717","abstract_canon_sha256":"c614915b7424a2f0b42cfaf25f5a05df4b9797af134aea3fd65d6a6a0c70fbee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:51.567115Z","signature_b64":"g+4SmK3lwBr29s7dJ/wbsZlbHlB+XAbbdCzdI70MkrkSQvgXO3mqtQWfJ5ZT+OpnZfPwnyDEEZjR1Jb42qdVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9b7d846ac5e952cb6a77420e05ac303fe0ac0785adfc83be2fb931317c73cb8","last_reissued_at":"2026-05-18T02:47:51.566614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:51.566614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hybrid moments of the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2008-03-16T14:12:09Z","abstract_excerpt":"The \"hybrid\" moments $$ \\int_T^{2T}|\\zeta(1/2+it)|^k{(\\int_{t-G}^{t+G}|\\zeta(1/2+ix)|^\\ell dx)}^m dt $$ of the Riemann zeta-function $\\zeta(s)$ on the critical line $\\Re s = 1/2$ are studied. The expected upper bound for the above expression is $O_\\epsilon(T^{1+\\epsilon}G^m)$. This is shown to be true for certain specific values of the natural numbers $k,\\ell,m$, and the explicitly determined range of $G = G(T;k,\\ell,m)$. The application to a mean square bound for the Mellin transform function of $|\\zeta(1/2+ix)|^4$ is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.2353","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":"0803.2353","created_at":"2026-05-18T02:47:51.566691+00:00"},{"alias_kind":"arxiv_version","alias_value":"0803.2353v2","created_at":"2026-05-18T02:47:51.566691+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.2353","created_at":"2026-05-18T02:47:51.566691+00:00"},{"alias_kind":"pith_short_12","alias_value":"7G35QRVML2KS","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"7G35QRVML2KSZNVH","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"7G35QRVM","created_at":"2026-05-18T12:25:56.245647+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/7G35QRVML2KSZNVHOQQOAWWDAP","json":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP.json","graph_json":"https://pith.science/api/pith-number/7G35QRVML2KSZNVHOQQOAWWDAP/graph.json","events_json":"https://pith.science/api/pith-number/7G35QRVML2KSZNVHOQQOAWWDAP/events.json","paper":"https://pith.science/paper/7G35QRVM"},"agent_actions":{"view_html":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP","download_json":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP.json","view_paper":"https://pith.science/paper/7G35QRVM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0803.2353&json=true","fetch_graph":"https://pith.science/api/pith-number/7G35QRVML2KSZNVHOQQOAWWDAP/graph.json","fetch_events":"https://pith.science/api/pith-number/7G35QRVML2KSZNVHOQQOAWWDAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP/action/storage_attestation","attest_author":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP/action/author_attestation","sign_citation":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP/action/citation_signature","submit_replication":"https://pith.science/pith/7G35QRVML2KSZNVHOQQOAWWDAP/action/replication_record"}},"created_at":"2026-05-18T02:47:51.566691+00:00","updated_at":"2026-05-18T02:47:51.566691+00:00"}