{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AERTHDMXXLFYD3Z6JELWVHGCJN","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":"46fd06082b581d5f9379b34d2056843d6e8867e8422a29deb0d59d6839ed0bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-04T22:18:14Z","title_canon_sha256":"c8d143a8011b608de355ac5281249b3ac0605981a143043f8df8539aa1861c9e"},"schema_version":"1.0","source":{"id":"1402.0900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0900","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0900v2","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0900","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"AERTHDMXXLFY","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AERTHDMXXLFYD3Z6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AERTHDMX","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:3fe83c14585a357d84429920f93c98a71c9b3ec5a4cb56c3e8aa8b29131a2b29","target":"graph","created_at":"2026-05-18T02:28:05Z","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 $f \\in S_{\\kappa}(\\Gamma_0(N))$ be a Hecke eigenform at $p$ with eigenvalue $\\lambda_f(p)$ for a prime $p$ not dividing $N$. Let $\\alpha_p$ and $\\beta_p$ be complex numbers satisfying $\\alpha_p + \\beta_p = \\lambda_f(p)$ and $\\alpha_p \\beta_p = p^{\\kappa-1}$. We calculate the norm of $f_{p}^{\\alpha_p}(z) = f(z) - \\beta_{p} f(pz)$ as well as the norm of $U_p f$, both classically and adelically. We use these results along with some convergence properties of the Euler product defining the symmetric square L-function of $f$ to give a `local' factorization of the Petersson norm of $f$.","authors_text":"Jim Brown, Krzysztof Klosin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-04T22:18:14Z","title":"On the norms of $p$-stabilized elliptic newforms (with an appendix by Keith Conrad)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0900","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":"sha256:2f427ffb3f994bc5d4ef70d5dafb216c417329397ea000572f1a70a232aac63d","target":"record","created_at":"2026-05-18T02:28:05Z","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":"46fd06082b581d5f9379b34d2056843d6e8867e8422a29deb0d59d6839ed0bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-04T22:18:14Z","title_canon_sha256":"c8d143a8011b608de355ac5281249b3ac0605981a143043f8df8539aa1861c9e"},"schema_version":"1.0","source":{"id":"1402.0900","kind":"arxiv","version":2}},"canonical_sha256":"0123338d97bacb81ef3e49176a9cc24b54c99d4171ac6efa84393b6e70063254","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0123338d97bacb81ef3e49176a9cc24b54c99d4171ac6efa84393b6e70063254","first_computed_at":"2026-05-18T02:28:05.418743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:05.418743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OcBEUd2yaKTuiU3AkzpW6THwbOWuDTXBCcZpj0r1UHQIBuVGrc1ZsltXf1ADt80ac0i+PnpWFz25+SOwJdrMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:05.419295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f427ffb3f994bc5d4ef70d5dafb216c417329397ea000572f1a70a232aac63d","sha256:3fe83c14585a357d84429920f93c98a71c9b3ec5a4cb56c3e8aa8b29131a2b29"],"state_sha256":"41333bdb3270cc2367fa3cd08c22ce6500ee67660e9fbd82236ec7f575de3afb"}