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Let $\\zeta$ denote the Riemann zeta function and $\\alpha_0=1.48\\ldots$ the unique positive solution of the equation $\\alpha\\zeta(1+\\alpha)=2$. We obtain sharp upper bounds for the norm of $\\mathscr{C}_\\varphi$ on $\\mathscr{H}^2$ when $0<\\operatorname{Re}\\varphi(+\\infty)-1/2 \\leq \\alpha_0$, by relating such sharp upper bounds to "},"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":"1705.01316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-03T09:05:29Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"eaf5153b21a6bc6424275db0c32482a5a28d217355796235bc4492970abb7508","abstract_canon_sha256":"1fa99e6e723703c12a9bb800811e5cdaeacb26c0150e61fb4f4f5e5c5e551e95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:46.713011Z","signature_b64":"1NztNyxUehlXShHp4GBN3guOk/bWBupjdbR9mKbD0CnYxJhSR20vAiIYSEHwIBU62gRHZ2sqVxv3mXGSCt0mDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1289e95bcbaa6dab0aaf091d3f7a2893eef6a7d85f1d11311d95aedf61bacc2","last_reissued_at":"2026-05-18T00:27:46.712380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:46.712380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp norm estimates for composition operators and Hilbert-type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Ole Fredrik Brevig","submitted_at":"2017-05-03T09:05:29Z","abstract_excerpt":"Let $\\mathscr{H}^2$ denote the Hardy space of Dirichlet series $f(s) = \\sum_{n\\geq1} a_n n^{-s}$ with square summable coefficients and suppose that $\\varphi$ is a symbol generating a composition operator on $\\mathscr{H}^2$ by $\\mathscr{C}_\\varphi(f) = f \\circ \\varphi$. Let $\\zeta$ denote the Riemann zeta function and $\\alpha_0=1.48\\ldots$ the unique positive solution of the equation $\\alpha\\zeta(1+\\alpha)=2$. We obtain sharp upper bounds for the norm of $\\mathscr{C}_\\varphi$ on $\\mathscr{H}^2$ when $0<\\operatorname{Re}\\varphi(+\\infty)-1/2 \\leq \\alpha_0$, by relating such sharp upper bounds to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01316","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.01316","created_at":"2026-05-18T00:27:46.712476+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.01316v2","created_at":"2026-05-18T00:27:46.712476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01316","created_at":"2026-05-18T00:27:46.712476+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EUJ5FN4XKTN","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EUJ5FN4XKTNVMFK","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EUJ5FN4","created_at":"2026-05-18T12:30:55.937587+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/2EUJ5FN4XKTNVMFK6CI5H55CRE","json":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE.json","graph_json":"https://pith.science/api/pith-number/2EUJ5FN4XKTNVMFK6CI5H55CRE/graph.json","events_json":"https://pith.science/api/pith-number/2EUJ5FN4XKTNVMFK6CI5H55CRE/events.json","paper":"https://pith.science/paper/2EUJ5FN4"},"agent_actions":{"view_html":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE","download_json":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE.json","view_paper":"https://pith.science/paper/2EUJ5FN4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.01316&json=true","fetch_graph":"https://pith.science/api/pith-number/2EUJ5FN4XKTNVMFK6CI5H55CRE/graph.json","fetch_events":"https://pith.science/api/pith-number/2EUJ5FN4XKTNVMFK6CI5H55CRE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE/action/storage_attestation","attest_author":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE/action/author_attestation","sign_citation":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE/action/citation_signature","submit_replication":"https://pith.science/pith/2EUJ5FN4XKTNVMFK6CI5H55CRE/action/replication_record"}},"created_at":"2026-05-18T00:27:46.712476+00:00","updated_at":"2026-05-18T00:27:46.712476+00:00"}