{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4CCIEZ4RFHAITXMJQMNWXOVPAX","short_pith_number":"pith:4CCIEZ4R","canonical_record":{"source":{"id":"1712.00363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-30T14:04:14Z","cross_cats_sorted":[],"title_canon_sha256":"a4c35b7613c1e09ebdfffb213d4c2686632bf032cb2db3265d53fa97448c14a0","abstract_canon_sha256":"0c00e415338f7764aaf4b60b56617d739aee319772948773e8c95f3959008268"},"schema_version":"1.0"},"canonical_sha256":"e08482679129c089dd89831b6bbaaf05f5cd957139511ece5f1adefbef9de58d","source":{"kind":"arxiv","id":"1712.00363","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00363","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00363v1","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00363","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"4CCIEZ4RFHAI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4CCIEZ4RFHAITXMJ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4CCIEZ4R","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4CCIEZ4RFHAITXMJQMNWXOVPAX","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-30T14:04:14Z","cross_cats_sorted":[],"title_canon_sha256":"a4c35b7613c1e09ebdfffb213d4c2686632bf032cb2db3265d53fa97448c14a0","abstract_canon_sha256":"0c00e415338f7764aaf4b60b56617d739aee319772948773e8c95f3959008268"},"schema_version":"1.0"},"canonical_sha256":"e08482679129c089dd89831b6bbaaf05f5cd957139511ece5f1adefbef9de58d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:06.433648Z","signature_b64":"OjFNN83rDCspboQ/cAmJRJTRIYofJzhHXILs/Uih/ODbGRes6s5XXa0Qz50AtYthExU3MfvaSmqv8VvfleCOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e08482679129c089dd89831b6bbaaf05f5cd957139511ece5f1adefbef9de58d","last_reissued_at":"2026-05-18T00:29:06.432971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:06.432971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00363","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ewt75gese59Oz3lUoMFCYZPk8kLeC0qGeUM8B9g2ADrR8iROpw/GR6JJvuh+PMCQiiX5IlIAbWy1TgdwaxZoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T22:37:20.421770Z"},"content_sha256":"3112f6f9439b0a5974713e51d1cfa064dc8ce39c3c7b3d74a407ca878c1d481e","schema_version":"1.0","event_id":"sha256:3112f6f9439b0a5974713e51d1cfa064dc8ce39c3c7b3d74a407ca878c1d481e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4CCIEZ4RFHAITXMJQMNWXOVPAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subconvexity Bound for Hecke character $L$-Functions of Imaginary quadratic Number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Keshav Aggarwal","submitted_at":"2017-11-30T14:04:14Z","abstract_excerpt":"Let $K=\\mathbb{Q}(\\sqrt{-D})$ be an imaginary number field, $(p)=\\mathfrak{p}\\mathfrak{p}'$ be a split odd prime and $\\psi$ be a Hecke character of conductor $\\mathfrak{p}$. Let $L(s,\\psi)$ be the associated $L$-function. We prove the Burgess bound in $t$-aspect and a hybrid bound in conductor aspect, \\begin{equation*} L(1/2+it,\\psi)\\ll_{D,\\varepsilon} (1+|t|)^{3/8+\\varepsilon}p^{1/8} \\end{equation*} for $p\\ll t$. In Appendix A, we present the ideas for an elementary proof of Voronoi summation formula for holomorphic cusp forms with CM and squarefree level. This is done by exploiting the latti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00363","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bl3j15iHdrdkOdnNckdv0Of/7bQsWrJL/zKA0gIpLqybpcQALMuzgcycGATlaW0HohldIct9gshPIeXbJIVPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T22:37:20.422117Z"},"content_sha256":"64464381232689d2fffd34ae965891ebb148b129573e3c67d6ea7545dd83b276","schema_version":"1.0","event_id":"sha256:64464381232689d2fffd34ae965891ebb148b129573e3c67d6ea7545dd83b276"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CCIEZ4RFHAITXMJQMNWXOVPAX/bundle.json","state_url":"https://pith.science/pith/4CCIEZ4RFHAITXMJQMNWXOVPAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CCIEZ4RFHAITXMJQMNWXOVPAX/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":"2026-07-03T22:37:20Z","links":{"resolver":"https://pith.science/pith/4CCIEZ4RFHAITXMJQMNWXOVPAX","bundle":"https://pith.science/pith/4CCIEZ4RFHAITXMJQMNWXOVPAX/bundle.json","state":"https://pith.science/pith/4CCIEZ4RFHAITXMJQMNWXOVPAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CCIEZ4RFHAITXMJQMNWXOVPAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4CCIEZ4RFHAITXMJQMNWXOVPAX","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":"0c00e415338f7764aaf4b60b56617d739aee319772948773e8c95f3959008268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-30T14:04:14Z","title_canon_sha256":"a4c35b7613c1e09ebdfffb213d4c2686632bf032cb2db3265d53fa97448c14a0"},"schema_version":"1.0","source":{"id":"1712.00363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00363","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00363v1","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00363","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"4CCIEZ4RFHAI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4CCIEZ4RFHAITXMJ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4CCIEZ4R","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:64464381232689d2fffd34ae965891ebb148b129573e3c67d6ea7545dd83b276","target":"graph","created_at":"2026-05-18T00:29:06Z","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":"Let $K=\\mathbb{Q}(\\sqrt{-D})$ be an imaginary number field, $(p)=\\mathfrak{p}\\mathfrak{p}'$ be a split odd prime and $\\psi$ be a Hecke character of conductor $\\mathfrak{p}$. Let $L(s,\\psi)$ be the associated $L$-function. We prove the Burgess bound in $t$-aspect and a hybrid bound in conductor aspect, \\begin{equation*} L(1/2+it,\\psi)\\ll_{D,\\varepsilon} (1+|t|)^{3/8+\\varepsilon}p^{1/8} \\end{equation*} for $p\\ll t$. In Appendix A, we present the ideas for an elementary proof of Voronoi summation formula for holomorphic cusp forms with CM and squarefree level. This is done by exploiting the latti","authors_text":"Keshav Aggarwal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-30T14:04:14Z","title":"Subconvexity Bound for Hecke character $L$-Functions of Imaginary quadratic Number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00363","kind":"arxiv","version":1},"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":"sha256:3112f6f9439b0a5974713e51d1cfa064dc8ce39c3c7b3d74a407ca878c1d481e","target":"record","created_at":"2026-05-18T00:29:06Z","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":"0c00e415338f7764aaf4b60b56617d739aee319772948773e8c95f3959008268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-30T14:04:14Z","title_canon_sha256":"a4c35b7613c1e09ebdfffb213d4c2686632bf032cb2db3265d53fa97448c14a0"},"schema_version":"1.0","source":{"id":"1712.00363","kind":"arxiv","version":1}},"canonical_sha256":"e08482679129c089dd89831b6bbaaf05f5cd957139511ece5f1adefbef9de58d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e08482679129c089dd89831b6bbaaf05f5cd957139511ece5f1adefbef9de58d","first_computed_at":"2026-05-18T00:29:06.432971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:06.432971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OjFNN83rDCspboQ/cAmJRJTRIYofJzhHXILs/Uih/ODbGRes6s5XXa0Qz50AtYthExU3MfvaSmqv8VvfleCOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:06.433648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3112f6f9439b0a5974713e51d1cfa064dc8ce39c3c7b3d74a407ca878c1d481e","sha256:64464381232689d2fffd34ae965891ebb148b129573e3c67d6ea7545dd83b276"],"state_sha256":"8dbd30dba938a43bd749a3d7ba551897db46e8518cfc25bf1e779c60b38b539e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u2gXU3ZI9XIn0L+b/cNXTsHv0+FMlHZ+6QWoTbOCLk8uwN94X1M1trSO1/2JLUyn+DHL7iJz/dQteo53eH3qCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T22:37:20.424227Z","bundle_sha256":"ef3f569191b7e2cda9c42466a7ffe52446854a2d09bf8106489ca162c5c8b815"}}