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In this paper, we establish an asymptotic formula of the seventh-power moment of $\\Delta(x)$ and prove that \\begin{equation*}\n  \\int_2^T \\Delta^7(x)\\mathrm{d}x=\n  \\frac{7(5s_{7;3}(d)-3s_{7;2}(d)-s_{7;1}(d))}{2816\\pi^7}T^{11/4}+O(T^{11/4-\\delta_7+\\varepsilon}) \\end{equation*} with $\\delta_7=1/336,$ which improves the previous result."},"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":"1601.05515","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-21T05:36:57Z","cross_cats_sorted":[],"title_canon_sha256":"8782298c817bfca72ee6517f828052411246122c1d8f74e3528e21f95086b803","abstract_canon_sha256":"acc65a7dd9b2ccd7284deb4d74f72a5697ddf6fe424b946a9080b57251451997"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:13.637393Z","signature_b64":"jDi9l8eyttaI2fXZxKTsx6WfEayb5JR8xaCdg/wbh7Wk5UVTiOpbeMXaTuD4Cw0/Ht89EuH2dFw4eF6bFK6mBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e660c93801705e483964e1aea12a2aadb53dcaba4f1c7ec8e6fbb5db6e2e564c","last_reissued_at":"2026-05-18T01:22:13.636989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:13.636989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Seventh Power Moment of $\\Delta(x)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinjiang Li","submitted_at":"2016-01-21T05:36:57Z","abstract_excerpt":"Let $\\Delta(x)$ be the error term of the Dirichlet divisor problem. In this paper, we establish an asymptotic formula of the seventh-power moment of $\\Delta(x)$ and prove that \\begin{equation*}\n  \\int_2^T \\Delta^7(x)\\mathrm{d}x=\n  \\frac{7(5s_{7;3}(d)-3s_{7;2}(d)-s_{7;1}(d))}{2816\\pi^7}T^{11/4}+O(T^{11/4-\\delta_7+\\varepsilon}) \\end{equation*} with $\\delta_7=1/336,$ which improves the previous result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05515","kind":"arxiv","version":1},"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":"1601.05515","created_at":"2026-05-18T01:22:13.637050+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.05515v1","created_at":"2026-05-18T01:22:13.637050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05515","created_at":"2026-05-18T01:22:13.637050+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ZQMSOABOBPE","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ZQMSOABOBPEQOLE","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ZQMSOAB","created_at":"2026-05-18T12:29:58.707656+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/4ZQMSOABOBPEQOLE4GXKCKRKVW","json":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW.json","graph_json":"https://pith.science/api/pith-number/4ZQMSOABOBPEQOLE4GXKCKRKVW/graph.json","events_json":"https://pith.science/api/pith-number/4ZQMSOABOBPEQOLE4GXKCKRKVW/events.json","paper":"https://pith.science/paper/4ZQMSOAB"},"agent_actions":{"view_html":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW","download_json":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW.json","view_paper":"https://pith.science/paper/4ZQMSOAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.05515&json=true","fetch_graph":"https://pith.science/api/pith-number/4ZQMSOABOBPEQOLE4GXKCKRKVW/graph.json","fetch_events":"https://pith.science/api/pith-number/4ZQMSOABOBPEQOLE4GXKCKRKVW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW/action/storage_attestation","attest_author":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW/action/author_attestation","sign_citation":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW/action/citation_signature","submit_replication":"https://pith.science/pith/4ZQMSOABOBPEQOLE4GXKCKRKVW/action/replication_record"}},"created_at":"2026-05-18T01:22:13.637050+00:00","updated_at":"2026-05-18T01:22:13.637050+00:00"}