{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RP5FAB6HIFS2FOECRXVV2ZTVW7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf7c39977b447f4d5d8425cc2beac3cfb16ff505b13948141636e7ccaaf2b8b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-26T07:50:10Z","title_canon_sha256":"93a4b894700f405f0c844ae308c1019d856ea85ffb758633bc41bd793aa1f720"},"schema_version":"1.0","source":{"id":"1508.06394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06394","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06394v1","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06394","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"RP5FAB6HIFS2","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RP5FAB6HIFS2FOEC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RP5FAB6H","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:4f0c01e96db638cb60b51458480adb801c36e2ff3c7e048a1d586381022866dc","target":"graph","created_at":"2026-05-18T00:58:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $d(n)$ be the number of divisors of $n$, let $$ \\Delta(x) := \\sum_{n\\le x}d(n) - x(\\log x + 2\\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\\zeta(s)$ denote the Riemann zeta-function. Several upper bounds for integrals of the type $$ \\int_0^T\\Delta^k(t)|\\zeta(1/2+it)|^{2m}dt \\qquad(k,m\\in\\Bbb N) $$ are given. This complements the results of the paper Ivi\\'c-Zhai [Indag. Math. 2015], where asymptotic formulas for $2\\le k \\le 8,m =1$ were established for the above integral.","authors_text":"Aleksandar Ivi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-26T07:50:10Z","title":"On some upper bounds for the zeta-function and the Dirichlet divisor problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06394","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa591c93a36a02276ad41786e4e2cab3b81accdbfaa6f14f7bd63643269e5eaa","target":"record","created_at":"2026-05-18T00:58:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf7c39977b447f4d5d8425cc2beac3cfb16ff505b13948141636e7ccaaf2b8b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-26T07:50:10Z","title_canon_sha256":"93a4b894700f405f0c844ae308c1019d856ea85ffb758633bc41bd793aa1f720"},"schema_version":"1.0","source":{"id":"1508.06394","kind":"arxiv","version":1}},"canonical_sha256":"8bfa5007c74165a2b8828deb5d6675b7e86aa941a94c9b80839bc3cadc305b45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bfa5007c74165a2b8828deb5d6675b7e86aa941a94c9b80839bc3cadc305b45","first_computed_at":"2026-05-18T00:58:55.494602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:55.494602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WGJC8yeaK9xoKQMmcs981K6p8ZfWUsTrhvJZWKDTjcS1YNS5lkEg248Fj6dCujMDleR1PIZ7A8ZQIPXVpOG5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:55.495253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa591c93a36a02276ad41786e4e2cab3b81accdbfaa6f14f7bd63643269e5eaa","sha256:4f0c01e96db638cb60b51458480adb801c36e2ff3c7e048a1d586381022866dc"],"state_sha256":"b54167c6c657ca171b035d27ba7fbe44ca8bcaa0c7e6bb451b1f9d3df2ca3cbb"}