{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YGVKUW6ASG3WQY5XPCBYQTY65B","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":"a8f7970ccdb48c1f6242a1978a622f6c887c13b50964712632dd0384f70e3490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","title_canon_sha256":"bbf5edc1f8ad351a449b6372c1b986169280d2f7b7783f3cbae64e74b7e9c396"},"schema_version":"1.0","source":{"id":"1710.10491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10491","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10491v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10491","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"YGVKUW6ASG3W","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YGVKUW6ASG3WQY5X","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YGVKUW6A","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:dfa2d4835737ef8fc396c6ec964fd6e9fc369d1c7606564784effcb382bf689c","target":"graph","created_at":"2026-05-18T00:31:49Z","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 $r,n$ be two natural numbers and let $H(r,n)$ denote the maximal absolute value of $r$th coefficient of divisors of $x^n-1$. In this paper, we show that $\\sum_{n\\leq x}H(r,n)$ is asymptotically equal to $c(r)x(\\log x)^{2^r-1}$ for some constant $c(r)>0$. Furthermore, we give an explicit expression of $c(r)$ in terms of $r$.","authors_text":"Sai Teja Somu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","title":"On $rth$ coefficient of divisors of $x^n-1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10491","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":"sha256:95ba2a113f06cb79af660f2f6aa0728b053f82ceecb65dde3849e6d75fc6db5d","target":"record","created_at":"2026-05-18T00:31:49Z","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":"a8f7970ccdb48c1f6242a1978a622f6c887c13b50964712632dd0384f70e3490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","title_canon_sha256":"bbf5edc1f8ad351a449b6372c1b986169280d2f7b7783f3cbae64e74b7e9c396"},"schema_version":"1.0","source":{"id":"1710.10491","kind":"arxiv","version":1}},"canonical_sha256":"c1aaaa5bc091b76863b77883884f1ee857d8f010ee61148df84820d9aabd079d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1aaaa5bc091b76863b77883884f1ee857d8f010ee61148df84820d9aabd079d","first_computed_at":"2026-05-18T00:31:49.359330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:49.359330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hkUskvWqiK7IT2ejb+9Rl9eTT53jgOVvjOq23DzWPBIjJmhL8JmuavKBBj5QWWiENkVoeoAC0VosmiBdI9UrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:49.359926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95ba2a113f06cb79af660f2f6aa0728b053f82ceecb65dde3849e6d75fc6db5d","sha256:dfa2d4835737ef8fc396c6ec964fd6e9fc369d1c7606564784effcb382bf689c"],"state_sha256":"494b95cf8dc3837855a2b1510590f3044cc69110a9f1eaa6833aa2e30a5c541a"}