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Consider the $d_{2k}$-dimensional space of cusp forms $\\mathcal{S}_{2k}^{\\Gamma}$ of weight $2k$ for $\\Gamma$, and let $\\{f_{1},\\ldots,f_{d_{2k}}\\}$ be an orthonormal basis of $\\mathcal{S}_{2k}^{\\Gamma}$ with respect to the Petersson inner product. In this paper we will give effective upper and lower bounds for the supremum of the quantity $S_{2k}^{\\Gamma}(z):=\\sum_{j=1}^{d_{2k}}\\vert f_{j}(z)\\vert^{2}\\,\\mathrm{Im}(z)^{2k}$ as $z$ ranges through $\\mathbb{H}$."},"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":"1801.05740","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-17T16:33:16Z","cross_cats_sorted":[],"title_canon_sha256":"70e7e07953c761c72ac93c498d4aca3c2ee6bae17ae3e0ad01ac88af7ca51077","abstract_canon_sha256":"7a6b3210b0690120d446a52937a59a471e82826a7679c75574ac8868b9ae9578"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:40.330567Z","signature_b64":"dUJHhBEA577V1N5iFpc3hPGKR9jjbYJCDt7jrViQXscnIsF0ZJOSW5yNMI+9jB8RX+xCC9BvPpZJIgYTA+V/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cbfeb86a196aa80e7c91fb11260b1d55dc10aac51a403947f4f6d76232f93fc","last_reissued_at":"2026-05-18T00:25:40.329909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:40.329909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Effective sup-norm bounds on average for cusp forms of even weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jay Jorgenson, Joshua S. Friedman, J\\\"urg Kramer","submitted_at":"2018-01-17T16:33:16Z","abstract_excerpt":"Let $\\Gamma\\subset\\mathrm{PSL}_{2}(\\mathbb{R})$ be a Fuchsian subgroup of the first kind acting on the upper half-plane $\\mathbb{H}$. Consider the $d_{2k}$-dimensional space of cusp forms $\\mathcal{S}_{2k}^{\\Gamma}$ of weight $2k$ for $\\Gamma$, and let $\\{f_{1},\\ldots,f_{d_{2k}}\\}$ be an orthonormal basis of $\\mathcal{S}_{2k}^{\\Gamma}$ with respect to the Petersson inner product. In this paper we will give effective upper and lower bounds for the supremum of the quantity $S_{2k}^{\\Gamma}(z):=\\sum_{j=1}^{d_{2k}}\\vert f_{j}(z)\\vert^{2}\\,\\mathrm{Im}(z)^{2k}$ as $z$ ranges through $\\mathbb{H}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05740","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":"1801.05740","created_at":"2026-05-18T00:25:40.330000+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.05740v1","created_at":"2026-05-18T00:25:40.330000+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05740","created_at":"2026-05-18T00:25:40.330000+00:00"},{"alias_kind":"pith_short_12","alias_value":"LS76XBVBS2VI","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LS76XBVBS2VIBZ6J","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LS76XBVB","created_at":"2026-05-18T12:32:37.024351+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/LS76XBVBS2VIBZ6JD6YREYFR2V","json":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V.json","graph_json":"https://pith.science/api/pith-number/LS76XBVBS2VIBZ6JD6YREYFR2V/graph.json","events_json":"https://pith.science/api/pith-number/LS76XBVBS2VIBZ6JD6YREYFR2V/events.json","paper":"https://pith.science/paper/LS76XBVB"},"agent_actions":{"view_html":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V","download_json":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V.json","view_paper":"https://pith.science/paper/LS76XBVB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.05740&json=true","fetch_graph":"https://pith.science/api/pith-number/LS76XBVBS2VIBZ6JD6YREYFR2V/graph.json","fetch_events":"https://pith.science/api/pith-number/LS76XBVBS2VIBZ6JD6YREYFR2V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V/action/storage_attestation","attest_author":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V/action/author_attestation","sign_citation":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V/action/citation_signature","submit_replication":"https://pith.science/pith/LS76XBVBS2VIBZ6JD6YREYFR2V/action/replication_record"}},"created_at":"2026-05-18T00:25:40.330000+00:00","updated_at":"2026-05-18T00:25:40.330000+00:00"}