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In this paper, we establish an asymptotic formula of the fourth power moment of $A(x)$ and prove that \\begin{equation*}\n  \\int_1^TA^4(x)\\mathrm{d}x=\\frac{3}{64\\kappa\\pi^4}s_{4;2}(\\tilde{a}) T^{2\\kappa}+O\\big(T^{2\\kappa-\\delta_4+\\varepsilon}\\big) \\end{equation*} with $\\delta_4=1/8$, 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":"1702.00163","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-01T08:43:04Z","cross_cats_sorted":[],"title_canon_sha256":"ad933ceaead1db6dae703b437caf1e6cfc94b77ac47608f4dcfd8c2104b4d35e","abstract_canon_sha256":"581656cf964c8ead343db16c858c2a141f2433bc859259a5e340079c2eaab59a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:34.228374Z","signature_b64":"+LEhX5yBdjsuPuKu4FEmcTzrPD6cKU7uH2mDRpJFj6vkV3GIRLmdv9/4l8k3npuHGhHSCmNt9eAjFyRy1MyRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9879fa1131d5fc404f35e11fb3222d9a8c996961733da12d3eec9c759e6131cd","last_reissued_at":"2026-05-18T00:30:34.227812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:34.227812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Fourth Power Moment of Fourier Coefficients of Cusp Form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinjiang Li, Min Zhang, Panwang Wang","submitted_at":"2017-02-01T08:43:04Z","abstract_excerpt":"Let $a(n)$ be the Fourier coefficients of a holomorphic cusp form of weight $\\kappa=2n\\geqslant12$ for the full modular group and $A(x)=\\sum\\limits_{n\\leqslant x}a(n)$. In this paper, we establish an asymptotic formula of the fourth power moment of $A(x)$ and prove that \\begin{equation*}\n  \\int_1^TA^4(x)\\mathrm{d}x=\\frac{3}{64\\kappa\\pi^4}s_{4;2}(\\tilde{a}) T^{2\\kappa}+O\\big(T^{2\\kappa-\\delta_4+\\varepsilon}\\big) \\end{equation*} with $\\delta_4=1/8$, which improves the previous result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00163","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":"1702.00163","created_at":"2026-05-18T00:30:34.227911+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.00163v2","created_at":"2026-05-18T00:30:34.227911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00163","created_at":"2026-05-18T00:30:34.227911+00:00"},{"alias_kind":"pith_short_12","alias_value":"TB47UEJR2X6E","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"TB47UEJR2X6EATZV","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"TB47UEJR","created_at":"2026-05-18T12:31:43.269735+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/TB47UEJR2X6EATZV4EP3GIRNTK","json":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK.json","graph_json":"https://pith.science/api/pith-number/TB47UEJR2X6EATZV4EP3GIRNTK/graph.json","events_json":"https://pith.science/api/pith-number/TB47UEJR2X6EATZV4EP3GIRNTK/events.json","paper":"https://pith.science/paper/TB47UEJR"},"agent_actions":{"view_html":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK","download_json":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK.json","view_paper":"https://pith.science/paper/TB47UEJR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.00163&json=true","fetch_graph":"https://pith.science/api/pith-number/TB47UEJR2X6EATZV4EP3GIRNTK/graph.json","fetch_events":"https://pith.science/api/pith-number/TB47UEJR2X6EATZV4EP3GIRNTK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/action/storage_attestation","attest_author":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/action/author_attestation","sign_citation":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/action/citation_signature","submit_replication":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/action/replication_record"}},"created_at":"2026-05-18T00:30:34.227911+00:00","updated_at":"2026-05-18T00:30:34.227911+00:00"}