{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XI67SJFLWDUKTHNXRJYD5TB3DN","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":"aee364ad2925a467c33c799fe7006dfb39710d4d91e2d0a4edda4ee848165869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-04T01:45:07Z","title_canon_sha256":"16fca0b22d9ac654fecbe4d96deeaa7054c66ae2306bb9b88af0830600985476"},"schema_version":"1.0","source":{"id":"1512.01299","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01299","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01299v4","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01299","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"XI67SJFLWDUK","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XI67SJFLWDUKTHNX","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XI67SJFL","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:79d0602799a23175ba9771206b942e80501fee8724fab2e7344355794ee618ec","target":"graph","created_at":"2026-05-18T00:45:08Z","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 $f$ and $g$ be weight $k$ holomorphic cusp forms and let $S_f(n)$ and $S_g(n)$ denote the sums of their first $n$ Fourier coefficients. Hafner and Ivic [HI], building on Chandrasekharan and Narasimhan [CN], proved asymptotics for $\\sum_{n \\leq X} \\lvert S_f(n) \\rvert^2$ and proved that the Classical Conjecture, that $S_f(X) \\ll X^{\\frac{k-1}{2} + \\frac{1}{4} + \\epsilon}$, holds on average over long intervals.\n  In this paper, we introduce and obtain meromorphic continuations for the Dirichlet series $D(s, S_f \\times S_g) = \\sum S_f(n)\\overline{S_g(n)} n^{-(s+k-1)}$ and $D(s, S_f \\times \\ov","authors_text":"Alexander Walker, Chan Ieong Kuan, David Lowry-Duda, Thomas A. Hulse","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-04T01:45:07Z","title":"The Second Moment of Sums of Coefficients of Cusp Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01299","kind":"arxiv","version":4},"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":"sha256:40fd0c1361e943c7212becc3c592b4e693059b2556b30e1a32b5a290876ad5b7","target":"record","created_at":"2026-05-18T00:45:08Z","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":"aee364ad2925a467c33c799fe7006dfb39710d4d91e2d0a4edda4ee848165869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-04T01:45:07Z","title_canon_sha256":"16fca0b22d9ac654fecbe4d96deeaa7054c66ae2306bb9b88af0830600985476"},"schema_version":"1.0","source":{"id":"1512.01299","kind":"arxiv","version":4}},"canonical_sha256":"ba3df924abb0e8a99db78a703ecc3b1b4250f4931f06e41b37926eb4144ce6d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba3df924abb0e8a99db78a703ecc3b1b4250f4931f06e41b37926eb4144ce6d3","first_computed_at":"2026-05-18T00:45:08.522988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:08.522988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6pMNcm0uZeil/IR/EcXly8iNBK90L7JUCXq7sgXcZXHkZFzHpJxv3Otrxi0LB2TVfxSOSV75MxsiRn/vCDLtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:08.523515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01299","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40fd0c1361e943c7212becc3c592b4e693059b2556b30e1a32b5a290876ad5b7","sha256:79d0602799a23175ba9771206b942e80501fee8724fab2e7344355794ee618ec"],"state_sha256":"d33ad5a00aa2a4f4bb8c0440cf8fae761ba6731c05e591d465b8230d809f9144"}