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Spektor","submitted_at":"2012-08-19T01:45:15Z","abstract_excerpt":"We improve on the inequality $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq \\frac{1}{\\sqrt p}, {0.2 cm}p\\geq 1,}$ showing that $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq C(p) \\frac{\\sqrt{3/\\pi}}{\\sqrt p},}$ with $\\displaystyle{\\lim_{p\\longrightarrow \\infty} C(p)=1,}$ and indeed that {align*} \\displaystyle{\\lim_{p\\longrightarrow \\infty}\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt/ \\frac{\\sqrt{3/\\pi}}{\\sqrt p}=1.} {align*}"},"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":"1208.3799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-19T01:45:15Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5bce19a25fcb2b4232ba2d65123edd0b31e2ca4251277c352715ae526b0802e9","abstract_canon_sha256":"f9a3d701561ae2df75cef2f7c3f99574fbcd87a93129f15df24a2f04296badc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:26.186966Z","signature_b64":"k8MCqQxBu2bczggkUvHVmhhUs4igVDhMVKVKl18CcG2SHPX9YTAZ+MKQHMKyx/rOswOvm7/ZE1JFGNKTEtk7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36a1dc7f4c59a2d360e6192d7632368be10d3652104b7a9f2d5fe6f10808558b","last_reissued_at":"2026-05-18T03:48:26.186436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:26.186436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Proof Of The Asymptotic Limit Of The $Lp$ Norm Of The Sinc Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"R. 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Spektor","submitted_at":"2012-08-19T01:45:15Z","abstract_excerpt":"We improve on the inequality $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq \\frac{1}{\\sqrt p}, {0.2 cm}p\\geq 1,}$ showing that $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq C(p) \\frac{\\sqrt{3/\\pi}}{\\sqrt p},}$ with $\\displaystyle{\\lim_{p\\longrightarrow \\infty} C(p)=1,}$ and indeed that {align*} \\displaystyle{\\lim_{p\\longrightarrow \\infty}\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt/ \\frac{\\sqrt{3/\\pi}}{\\sqrt p}=1.} {align*}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3799","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":"1208.3799","created_at":"2026-05-18T03:48:26.186525+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3799v1","created_at":"2026-05-18T03:48:26.186525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3799","created_at":"2026-05-18T03:48:26.186525+00:00"},{"alias_kind":"pith_short_12","alias_value":"G2Q5Y72MLGRN","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"G2Q5Y72MLGRNGYHG","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"G2Q5Y72M","created_at":"2026-05-18T12:27:06.952714+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/G2Q5Y72MLGRNGYHGDEWXMMRWRP","json":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP.json","graph_json":"https://pith.science/api/pith-number/G2Q5Y72MLGRNGYHGDEWXMMRWRP/graph.json","events_json":"https://pith.science/api/pith-number/G2Q5Y72MLGRNGYHGDEWXMMRWRP/events.json","paper":"https://pith.science/paper/G2Q5Y72M"},"agent_actions":{"view_html":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP","download_json":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP.json","view_paper":"https://pith.science/paper/G2Q5Y72M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3799&json=true","fetch_graph":"https://pith.science/api/pith-number/G2Q5Y72MLGRNGYHGDEWXMMRWRP/graph.json","fetch_events":"https://pith.science/api/pith-number/G2Q5Y72MLGRNGYHGDEWXMMRWRP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP/action/storage_attestation","attest_author":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP/action/author_attestation","sign_citation":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP/action/citation_signature","submit_replication":"https://pith.science/pith/G2Q5Y72MLGRNGYHGDEWXMMRWRP/action/replication_record"}},"created_at":"2026-05-18T03:48:26.186525+00:00","updated_at":"2026-05-18T03:48:26.186525+00:00"}