{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TB47UEJR2X6EATZV4EP3GIRNTK","short_pith_number":"pith:TB47UEJR","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"},"canonical_sha256":"9879fa1131d5fc404f35e11fb3222d9a8c996961733da12d3eec9c759e6131cd","source":{"kind":"arxiv","id":"1702.00163","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00163","created_at":"2026-05-18T00:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00163v2","created_at":"2026-05-18T00:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00163","created_at":"2026-05-18T00:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"TB47UEJR2X6E","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"TB47UEJR2X6EATZV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"TB47UEJR","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TB47UEJR2X6EATZV4EP3GIRNTK","target":"record","payload":{"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"},"canonical_sha256":"9879fa1131d5fc404f35e11fb3222d9a8c996961733da12d3eec9c759e6131cd","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"},"source_kind":"arxiv","source_id":"1702.00163","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3oRkEzHRTPE8Zr9WJrc4UE/I4xklx/OS3kgT8eP0IMNKT+nSWAARgPRDHKTd/VC9RaRVV9NX1hCwO8G0vn7xAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:59:16.440238Z"},"content_sha256":"16cbe26df9b1723198ee47146ba96e173702fbb94c7fe4a4b1d3485896ee3e70","schema_version":"1.0","event_id":"sha256:16cbe26df9b1723198ee47146ba96e173702fbb94c7fe4a4b1d3485896ee3e70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TB47UEJR2X6EATZV4EP3GIRNTK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kO7HVzDmbrBLMcNHeu6NE5kzfxYKOCLSPB8K7WddmLxvlPIa0hTTXvnwjhq3nrYr4FNQQnHVjUOZWMZawwzCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:59:16.441000Z"},"content_sha256":"cd58b3c78e448deffc258409632ba365932c00b9ecd9ded27abd4eff1e6fcf66","schema_version":"1.0","event_id":"sha256:cd58b3c78e448deffc258409632ba365932c00b9ecd9ded27abd4eff1e6fcf66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/bundle.json","state_url":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TB47UEJR2X6EATZV4EP3GIRNTK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T20:59:16Z","links":{"resolver":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK","bundle":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/bundle.json","state":"https://pith.science/pith/TB47UEJR2X6EATZV4EP3GIRNTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TB47UEJR2X6EATZV4EP3GIRNTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TB47UEJR2X6EATZV4EP3GIRNTK","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":"581656cf964c8ead343db16c858c2a141f2433bc859259a5e340079c2eaab59a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-01T08:43:04Z","title_canon_sha256":"ad933ceaead1db6dae703b437caf1e6cfc94b77ac47608f4dcfd8c2104b4d35e"},"schema_version":"1.0","source":{"id":"1702.00163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00163","created_at":"2026-05-18T00:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00163v2","created_at":"2026-05-18T00:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00163","created_at":"2026-05-18T00:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"TB47UEJR2X6E","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"TB47UEJR2X6EATZV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"TB47UEJR","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:cd58b3c78e448deffc258409632ba365932c00b9ecd9ded27abd4eff1e6fcf66","target":"graph","created_at":"2026-05-18T00:30:34Z","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 $a(n)$ 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.","authors_text":"Jinjiang Li, Min Zhang, Panwang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-01T08:43:04Z","title":"On the Fourth Power Moment of Fourier Coefficients of Cusp Form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00163","kind":"arxiv","version":2},"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":"sha256:16cbe26df9b1723198ee47146ba96e173702fbb94c7fe4a4b1d3485896ee3e70","target":"record","created_at":"2026-05-18T00:30:34Z","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":"581656cf964c8ead343db16c858c2a141f2433bc859259a5e340079c2eaab59a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-01T08:43:04Z","title_canon_sha256":"ad933ceaead1db6dae703b437caf1e6cfc94b77ac47608f4dcfd8c2104b4d35e"},"schema_version":"1.0","source":{"id":"1702.00163","kind":"arxiv","version":2}},"canonical_sha256":"9879fa1131d5fc404f35e11fb3222d9a8c996961733da12d3eec9c759e6131cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9879fa1131d5fc404f35e11fb3222d9a8c996961733da12d3eec9c759e6131cd","first_computed_at":"2026-05-18T00:30:34.227812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:34.227812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+LEhX5yBdjsuPuKu4FEmcTzrPD6cKU7uH2mDRpJFj6vkV3GIRLmdv9/4l8k3npuHGhHSCmNt9eAjFyRy1MyRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:34.228374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16cbe26df9b1723198ee47146ba96e173702fbb94c7fe4a4b1d3485896ee3e70","sha256:cd58b3c78e448deffc258409632ba365932c00b9ecd9ded27abd4eff1e6fcf66"],"state_sha256":"a786710e38cf74b4f9b4e009b059b2407242e3e6cc513f18ee2c22fecf6d9aae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAUIIRfCcWsrie+Aji/w29wVqPzG55eNGzE/F5t709X7gTOWmHDZECHwf4WzzMkMWNkie9pyejjG9+1GGVMuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:59:16.445076Z","bundle_sha256":"d98a902eca18b56ebced185df58d7e8e787394582e9a15e96dd56735e5150296"}}