{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OJARMS66WDIUUGOGJQAALCSNZF","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":"77ad22df536db14c24e5e8f579f50fb31be99128cb2fb97583fff212430e495f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-22T13:38:54Z","title_canon_sha256":"bf50956356c3586d23b50022378024015a6af84b2a82511cb4b5e76fa870e87e"},"schema_version":"1.0","source":{"id":"1303.5617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5617","created_at":"2026-05-18T02:39:01Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5617v1","created_at":"2026-05-18T02:39:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5617","created_at":"2026-05-18T02:39:01Z"},{"alias_kind":"pith_short_12","alias_value":"OJARMS66WDIU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OJARMS66WDIUUGOG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OJARMS66","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:c3a5cbd0f96e38a5aece82f40f29869f1f1c00ca11dec7c19bfe46392ba58dce","target":"graph","created_at":"2026-05-18T02:39:01Z","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 v be a multiplicative arithmetic function with support of positive asymptotic density. We prove that for any not identically zero arithmetic function f such that \\sum_{f(n) \\neq 0} 1 / n < \\infty, the support of the Dirichlet convolution f * v possesses a positive asymptotic density. When f is a multiplicative function, we give also a quantitative version of this claim. This generalizes a previous result of P. Pollack and the author, concerning the support of M\\\"obius and Dirichlet transforms of arithmetic functions.","authors_text":"Carlo Sanna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-22T13:38:54Z","title":"On the asymptotic density of the support of a Dirichlet convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5617","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":"sha256:5a5271e5c8f97ceaaa4ec952918c4514182bbd7e5b0cc459ab8efcf396da3324","target":"record","created_at":"2026-05-18T02:39:01Z","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":"77ad22df536db14c24e5e8f579f50fb31be99128cb2fb97583fff212430e495f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-22T13:38:54Z","title_canon_sha256":"bf50956356c3586d23b50022378024015a6af84b2a82511cb4b5e76fa870e87e"},"schema_version":"1.0","source":{"id":"1303.5617","kind":"arxiv","version":1}},"canonical_sha256":"7241164bdeb0d14a19c64c00058a4dc9763a596a3c3d92b63bb92958fbd82d30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7241164bdeb0d14a19c64c00058a4dc9763a596a3c3d92b63bb92958fbd82d30","first_computed_at":"2026-05-18T02:39:01.370498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:01.370498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f5jpSoh6C88z8/ppRS+dgcRTl3gHnSo6RBo6/X18cJm2SnE7gij9OucVkcU39XVBlToJXZLhiYblGkQ15EvsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:01.370990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a5271e5c8f97ceaaa4ec952918c4514182bbd7e5b0cc459ab8efcf396da3324","sha256:c3a5cbd0f96e38a5aece82f40f29869f1f1c00ca11dec7c19bfe46392ba58dce"],"state_sha256":"59efa961e25025f4a3f50a46ee0ee0d584e99199655e1bbeaad5d45b38bdc425"}