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For complex scalars: $K_{n}\\leq\\frac{2}{\\sqrt{\\pi}}(n-1)^{0.304975}$.{enumerate} {0.1cm} \\noindent We also obtain sharper estimates for higher values of $n$. For instance, \\[ K_{n}<1.30379(n-1) ^{0.526322}\\] for real scalars and $n>2^{8}$ and \\[ K_{n}<0.99137(n-1) ^{0.304975}\\] for complex scalars and $n > 2^{15}.$"},"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":"1302.0517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-03T18:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"6091b31766f2f5fe1765687f795279221a96c456fca8bf94dfa9d5773412362d","abstract_canon_sha256":"c9ebf5153d155191f5bafa0d4db8b18fbff785eee3aa16af778904bdb0c2d88b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:36.934998Z","signature_b64":"dkTMzXcqHJ5ziFyIqxHExoGyhpjOwuHqAF4lcBy8Dasv6LIipEkyC0jVdlk5+j6l21+mZK/ZhBaN8kl5jG5GDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bce04b33ac7c1617b69bbe502e519b388a1d6ee8fb12f52311fdd3539919961","last_reissued_at":"2026-05-18T03:34:36.934473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:36.934473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the optimal multilinear Bohnenblust--Hille constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D.M. Serrano-Rodriguez, D. Nunez-Alarcon, D. Pellegrino, J.B. Seoane-Sepulveda","submitted_at":"2013-02-03T18:01:35Z","abstract_excerpt":"The upper estimates for the optimal constants of the multilinear Bohnenblust--Hille inequality obtained in [J. Funct. Anal. 264 (2013), 429--463] are here improved to: {0.1cm}\n  {enumerate} For real scalars: $K_{n}\\leq\\sqrt{2}(n-1)^{0.526322}$. For complex scalars: $K_{n}\\leq\\frac{2}{\\sqrt{\\pi}}(n-1)^{0.304975}$.{enumerate} {0.1cm} \\noindent We also obtain sharper estimates for higher values of $n$. For instance, \\[ K_{n}<1.30379(n-1) ^{0.526322}\\] for real scalars and $n>2^{8}$ and \\[ K_{n}<0.99137(n-1) ^{0.304975}\\] for complex scalars and $n > 2^{15}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0517","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":"1302.0517","created_at":"2026-05-18T03:34:36.934555+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.0517v1","created_at":"2026-05-18T03:34:36.934555+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0517","created_at":"2026-05-18T03:34:36.934555+00:00"},{"alias_kind":"pith_short_12","alias_value":"RPHAJMZ2Y7AW","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"RPHAJMZ2Y7AWC63J","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"RPHAJMZ2","created_at":"2026-05-18T12:27:59.945178+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/RPHAJMZ2Y7AWC63JXPSQFZIZWO","json":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO.json","graph_json":"https://pith.science/api/pith-number/RPHAJMZ2Y7AWC63JXPSQFZIZWO/graph.json","events_json":"https://pith.science/api/pith-number/RPHAJMZ2Y7AWC63JXPSQFZIZWO/events.json","paper":"https://pith.science/paper/RPHAJMZ2"},"agent_actions":{"view_html":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO","download_json":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO.json","view_paper":"https://pith.science/paper/RPHAJMZ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.0517&json=true","fetch_graph":"https://pith.science/api/pith-number/RPHAJMZ2Y7AWC63JXPSQFZIZWO/graph.json","fetch_events":"https://pith.science/api/pith-number/RPHAJMZ2Y7AWC63JXPSQFZIZWO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO/action/storage_attestation","attest_author":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO/action/author_attestation","sign_citation":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO/action/citation_signature","submit_replication":"https://pith.science/pith/RPHAJMZ2Y7AWC63JXPSQFZIZWO/action/replication_record"}},"created_at":"2026-05-18T03:34:36.934555+00:00","updated_at":"2026-05-18T03:34:36.934555+00:00"}