{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XDHC4U5HNSCF4W3EYXKKJHVZBW","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":"f20849c3915e7f032a313398a196b2f06cee4308bc9ba9d50115e358fa4a767e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-10T13:40:14Z","title_canon_sha256":"182df56a04cdcbb8e2edf21d870a691185a0467fdbed0606b67931a17ef6664e"},"schema_version":"1.0","source":{"id":"1812.03788","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03788","created_at":"2026-05-17T23:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03788v5","created_at":"2026-05-17T23:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03788","created_at":"2026-05-17T23:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"XDHC4U5HNSCF","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XDHC4U5HNSCF4W3E","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XDHC4U5H","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:7711afad78d4d2e33ca00bd1be74c3f34830f86b0388093de86b1f2df6d08b9a","target":"graph","created_at":"2026-05-17T23:41:53Z","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":"In recent years the question of maximizing GCD sums regained interest due to its firm link with large values of $L$-functions. In the present paper we initiate the study of minimizing for positive weights~$w$ of normalized $L^1$- norm the sum $\\sum_{m_1 , m_2 \\leqslant N} w({m_1})w({m_2})\\frac{(m_1,m_2)}{\\sqrt{m_1m_2}} $. We consider as well the intertwined question of minimizing a weighted version of the usual multiplicative energy. We give three applications of our results. Firstly we obtain a logarithmic refinement of Burgess' bound on character sums $\\displaystyle{\\sum_{M<n\\leqslant M+N}\\c","authors_text":"Marc Munsch, R\\'egis de la Bret\\`eche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-10T13:40:14Z","title":"Minimizing GCD sums and applications to non-vanishing of theta functions and to Burgess' inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03788","kind":"arxiv","version":5},"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":"sha256:6875424a367db3e3603c1fe17df745f6a962b786a93feb41f1a19d1abed7b314","target":"record","created_at":"2026-05-17T23:41:53Z","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":"f20849c3915e7f032a313398a196b2f06cee4308bc9ba9d50115e358fa4a767e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-10T13:40:14Z","title_canon_sha256":"182df56a04cdcbb8e2edf21d870a691185a0467fdbed0606b67931a17ef6664e"},"schema_version":"1.0","source":{"id":"1812.03788","kind":"arxiv","version":5}},"canonical_sha256":"b8ce2e53a76c845e5b64c5d4a49eb90d9cefadffed79c6cc74bad8631dce6ec7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8ce2e53a76c845e5b64c5d4a49eb90d9cefadffed79c6cc74bad8631dce6ec7","first_computed_at":"2026-05-17T23:41:53.633949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:53.633949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TKB88TT3i15DMlI54Rs76e5E9iKOw8x0ldvbAlebM3EMk+LkKmZyE09ykRobZDW0WqyLhkOl9ERCgsNDCUmICg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:53.634353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03788","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6875424a367db3e3603c1fe17df745f6a962b786a93feb41f1a19d1abed7b314","sha256:7711afad78d4d2e33ca00bd1be74c3f34830f86b0388093de86b1f2df6d08b9a"],"state_sha256":"de3a8d0dc38a6f3daf008624b726d67a4d501d79907a3596b77da3d2a1d2f3fb"}