{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OACQ3JMWJJ7UYUQ2BHXXAHCRXQ","short_pith_number":"pith:OACQ3JMW","canonical_record":{"source":{"id":"1405.6516","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:32:37Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"d261a028ccf9a830b4c45cd1ce34148d3fc990dded8aeaef4737bae07bb138e9","abstract_canon_sha256":"7d4195eb6be9b8842c570a0f9ab2ad820550c567a6b8c75b9746c4009766baba"},"schema_version":"1.0"},"canonical_sha256":"70050da5964a7f4c521a09ef701c51bc17060bb3fceb54c3f07edcdd376f1604","source":{"kind":"arxiv","id":"1405.6516","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6516","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6516v3","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6516","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"OACQ3JMWJJ7U","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OACQ3JMWJJ7UYUQ2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OACQ3JMW","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OACQ3JMWJJ7UYUQ2BHXXAHCRXQ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6516","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:32:37Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"d261a028ccf9a830b4c45cd1ce34148d3fc990dded8aeaef4737bae07bb138e9","abstract_canon_sha256":"7d4195eb6be9b8842c570a0f9ab2ad820550c567a6b8c75b9746c4009766baba"},"schema_version":"1.0"},"canonical_sha256":"70050da5964a7f4c521a09ef701c51bc17060bb3fceb54c3f07edcdd376f1604","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:20.802483Z","signature_b64":"7y9O4OvCF5em+lgPcAun8f++WECq40rjCwdnCNqnrdUvj6sQ9XVSvdCKzqWUUySU8JXZ3Wu02WDx+jcw1oWhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70050da5964a7f4c521a09ef701c51bc17060bb3fceb54c3f07edcdd376f1604","last_reissued_at":"2026-05-18T02:28:20.801940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:20.801940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6516","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JjimjaXi8ngWkHhmPymggMasfkO+wKIvT1/cEYEyZyODpNBnVW3sb8E9qF8fljdaShGmPXfYxtF/asmpMBooAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:21:37.259016Z"},"content_sha256":"ba3c7e400ca4a0036c73acd019e276391943c47619afd8741a8aa009748503c2","schema_version":"1.0","event_id":"sha256:ba3c7e400ca4a0036c73acd019e276391943c47619afd8741a8aa009748503c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OACQ3JMWJJ7UYUQ2BHXXAHCRXQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An inequality of Hardy--Littlewood type for Dirichlet polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.NT","authors_text":"Andriy Bondarenko, Kristian Seip, Winston Heap","submitted_at":"2014-05-26T09:32:37Z","abstract_excerpt":"The $L^q$ norm of a Dirichlet polynomial $F(s)=\\sum_{n=1}^{N} a_n n^{-s}$ is defined as \\[\\| F\\|_q:=(\\lim_{T\\to\\infty}\\frac{1}{T}\\int_{0}^T |F(it)|^qdt)^{1/q}\\] for $0<q<\\infty$. It is shown that \\[ (\\sum_{n=1}^{N} |a_n|^2|\\mu(n)|[d(n)]^{\\frac{\\log q}{\\log 2} -1})^{1/2}\\le \\| F\\|_q \\] when $0<q<2$; here $\\mu$ is the M\\\"{o}bius function and $d$ the divisor function. This result is used to prove that the $L^q$ norm of $D_N(s):=\\sum_{n=1}^{N} n^{-1/2-s}$ satisfies $\\|D_N\\|_q\\gg (\\log N)^{q/4}$ for $0<q<\\infty$. By Helson's generalization of the M. Riesz theorem on the conjugation operator, the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6516","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q5MzumvhNolChf5p2XGwN+xvzZ6b5JoRi3c0ak7xjoFOcNIbiYr2wM+CYSSiS9mNxjXyZaiRFXNcymBq9nzjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:21:37.259370Z"},"content_sha256":"c5478a013cfdea192db999ba08f6dddd53b87c875d2b94700459dceeb4bff354","schema_version":"1.0","event_id":"sha256:c5478a013cfdea192db999ba08f6dddd53b87c875d2b94700459dceeb4bff354"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OACQ3JMWJJ7UYUQ2BHXXAHCRXQ/bundle.json","state_url":"https://pith.science/pith/OACQ3JMWJJ7UYUQ2BHXXAHCRXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OACQ3JMWJJ7UYUQ2BHXXAHCRXQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T17:21:37Z","links":{"resolver":"https://pith.science/pith/OACQ3JMWJJ7UYUQ2BHXXAHCRXQ","bundle":"https://pith.science/pith/OACQ3JMWJJ7UYUQ2BHXXAHCRXQ/bundle.json","state":"https://pith.science/pith/OACQ3JMWJJ7UYUQ2BHXXAHCRXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OACQ3JMWJJ7UYUQ2BHXXAHCRXQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OACQ3JMWJJ7UYUQ2BHXXAHCRXQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7d4195eb6be9b8842c570a0f9ab2ad820550c567a6b8c75b9746c4009766baba","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:32:37Z","title_canon_sha256":"d261a028ccf9a830b4c45cd1ce34148d3fc990dded8aeaef4737bae07bb138e9"},"schema_version":"1.0","source":{"id":"1405.6516","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6516","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6516v3","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6516","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"OACQ3JMWJJ7U","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OACQ3JMWJJ7UYUQ2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OACQ3JMW","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:c5478a013cfdea192db999ba08f6dddd53b87c875d2b94700459dceeb4bff354","target":"graph","created_at":"2026-05-18T02:28:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The $L^q$ norm of a Dirichlet polynomial $F(s)=\\sum_{n=1}^{N} a_n n^{-s}$ is defined as \\[\\| F\\|_q:=(\\lim_{T\\to\\infty}\\frac{1}{T}\\int_{0}^T |F(it)|^qdt)^{1/q}\\] for $0<q<\\infty$. It is shown that \\[ (\\sum_{n=1}^{N} |a_n|^2|\\mu(n)|[d(n)]^{\\frac{\\log q}{\\log 2} -1})^{1/2}\\le \\| F\\|_q \\] when $0<q<2$; here $\\mu$ is the M\\\"{o}bius function and $d$ the divisor function. This result is used to prove that the $L^q$ norm of $D_N(s):=\\sum_{n=1}^{N} n^{-1/2-s}$ satisfies $\\|D_N\\|_q\\gg (\\log N)^{q/4}$ for $0<q<\\infty$. By Helson's generalization of the M. Riesz theorem on the conjugation operator, the re","authors_text":"Andriy Bondarenko, Kristian Seip, Winston Heap","cross_cats":["math.CV","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:32:37Z","title":"An inequality of Hardy--Littlewood type for Dirichlet polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6516","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ba3c7e400ca4a0036c73acd019e276391943c47619afd8741a8aa009748503c2","target":"record","created_at":"2026-05-18T02:28:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7d4195eb6be9b8842c570a0f9ab2ad820550c567a6b8c75b9746c4009766baba","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:32:37Z","title_canon_sha256":"d261a028ccf9a830b4c45cd1ce34148d3fc990dded8aeaef4737bae07bb138e9"},"schema_version":"1.0","source":{"id":"1405.6516","kind":"arxiv","version":3}},"canonical_sha256":"70050da5964a7f4c521a09ef701c51bc17060bb3fceb54c3f07edcdd376f1604","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70050da5964a7f4c521a09ef701c51bc17060bb3fceb54c3f07edcdd376f1604","first_computed_at":"2026-05-18T02:28:20.801940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:20.801940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7y9O4OvCF5em+lgPcAun8f++WECq40rjCwdnCNqnrdUvj6sQ9XVSvdCKzqWUUySU8JXZ3Wu02WDx+jcw1oWhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:20.802483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6516","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba3c7e400ca4a0036c73acd019e276391943c47619afd8741a8aa009748503c2","sha256:c5478a013cfdea192db999ba08f6dddd53b87c875d2b94700459dceeb4bff354"],"state_sha256":"0d59903c36e56956f624c04a9e95e2a9216eafe690ccbaa3ff2645cec014b4aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qyU+s0InOVmbOzX/0PVpSrspue02gfSQUutiGHSXSyEgd860JxbXu3pSXtZYAWoCnEtW4c1o8O+iyNMNwP5tDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:21:37.261334Z","bundle_sha256":"2bcdb2b02f1dd27d346082cadf4f861888d3349583ade4c1abd7c2397ac759b5"}}