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Consider the $d$-dimensional space of cusp forms $\\mathcal{S}_{k}^{\\Gamma}$ of weight $2k$ for $\\Gamma$, and let $\\{f_{1},\\ldots,f_{d}\\}$ be an orthonormal basis of $\\mathcal{S}_{k}^{\\Gamma}$ with respect to the Petersson inner product. In this paper we show that the sup-norm of the quantity $S_{k}^{\\Gamma}(z):=\\sum_{j=1}^{d}| f_{j}(z)|^{2}\\,\\mathrm{Im}(z)^{2k}$ is bounded as $O_{\\Gamma}(k)$ in the cocompact setting, and as $O_{\\Gamma}(k^{3/2})$ in the cofinit"},"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":"1305.1348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-06T22:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"adc738981d4f70ed6c10bb95a5657e691ebdb91b41fd55e4cdba9ef10b5442c6","abstract_canon_sha256":"7b527d8529f7a60de601e23bbdafe5ef94da8a22ff92115a1837be9b0721dd08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:21.987363Z","signature_b64":"9DqsbwFUldBgepFBUMQXYdkSzv+rwyVoBNhjCrouc3Q3cQrJFP1A5OBDR3XDUF0s0VfBclUHx31g30Cyv4WiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ca356996e6896b46af8148cc3ccaa0096b7ea83b2babf22b392e5dfe86f2552","last_reissued_at":"2026-05-18T03:26:21.986837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:21.986837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform sup-norm bounds on average for cusp forms of higher weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jay Jorgenson, Joshua S. 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In this paper we show that the sup-norm of the quantity $S_{k}^{\\Gamma}(z):=\\sum_{j=1}^{d}| f_{j}(z)|^{2}\\,\\mathrm{Im}(z)^{2k}$ is bounded as $O_{\\Gamma}(k)$ in the cocompact setting, and as $O_{\\Gamma}(k^{3/2})$ in the cofinit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1348","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":"1305.1348","created_at":"2026-05-18T03:26:21.986924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.1348v1","created_at":"2026-05-18T03:26:21.986924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1348","created_at":"2026-05-18T03:26:21.986924+00:00"},{"alias_kind":"pith_short_12","alias_value":"NSRVNGLONCLL","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NSRVNGLONCLLI2XY","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NSRVNGLO","created_at":"2026-05-18T12:27:52.871228+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/NSRVNGLONCLLI2XYCSGMHTFKAC","json":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC.json","graph_json":"https://pith.science/api/pith-number/NSRVNGLONCLLI2XYCSGMHTFKAC/graph.json","events_json":"https://pith.science/api/pith-number/NSRVNGLONCLLI2XYCSGMHTFKAC/events.json","paper":"https://pith.science/paper/NSRVNGLO"},"agent_actions":{"view_html":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC","download_json":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC.json","view_paper":"https://pith.science/paper/NSRVNGLO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.1348&json=true","fetch_graph":"https://pith.science/api/pith-number/NSRVNGLONCLLI2XYCSGMHTFKAC/graph.json","fetch_events":"https://pith.science/api/pith-number/NSRVNGLONCLLI2XYCSGMHTFKAC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC/action/storage_attestation","attest_author":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC/action/author_attestation","sign_citation":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC/action/citation_signature","submit_replication":"https://pith.science/pith/NSRVNGLONCLLI2XYCSGMHTFKAC/action/replication_record"}},"created_at":"2026-05-18T03:26:21.986924+00:00","updated_at":"2026-05-18T03:26:21.986924+00:00"}