{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O4ANV2LKQ7IZDTN4PR3JTJFXIX","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":"62164e6c11bfb2630a72573b3adce9c709c6be3e6aeb5608710715d6f3a9b378","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-09T22:47:19Z","title_canon_sha256":"16d394cfdb38e905a7f7e8a106059a342b2df761615b39a7e6d88f2079f270c3"},"schema_version":"1.0","source":{"id":"1411.2293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2293","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2293v1","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2293","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"O4ANV2LKQ7IZ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O4ANV2LKQ7IZDTN4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O4ANV2LK","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:e68e7aecbbe7858c6b4f9f9681f139a9f9bedca0482e8c194a2e9918ac829fa2","target":"graph","created_at":"2026-05-18T01:10:54Z","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":"Maier and Rassias computed the moments and proved a distribution result for the cotangent sum $c_0(a/q):=-\\sum_{m<q}\\frac mq\\cot(\\frac{\\pi ma}{q})$ on average over $1/2<A_0\\leq a/q<A_1<1$, as $q\\rightarrow \\infty$. We give a simple argument that recovers their results (with stronger error terms) and extends them to the full range $1\\leq a<q$. Moreover, we give a density result for $c_0$ and answer a question posed by Maier and Rassias on the growth of the moments of $c_0$.","authors_text":"Sandro Bettin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-09T22:47:19Z","title":"On the distribution of a cotangent sum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2293","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:bd655ea590f6653a78003c889c07eea26898d588d36241354dd02fa4c383ecae","target":"record","created_at":"2026-05-18T01:10:54Z","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":"62164e6c11bfb2630a72573b3adce9c709c6be3e6aeb5608710715d6f3a9b378","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-09T22:47:19Z","title_canon_sha256":"16d394cfdb38e905a7f7e8a106059a342b2df761615b39a7e6d88f2079f270c3"},"schema_version":"1.0","source":{"id":"1411.2293","kind":"arxiv","version":1}},"canonical_sha256":"7700dae96a87d191cdbc7c7699a4b745d24b5302743f181d852d5363050566a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7700dae96a87d191cdbc7c7699a4b745d24b5302743f181d852d5363050566a5","first_computed_at":"2026-05-18T01:10:54.590832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:54.590832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j6vqcC2/ivjFfCfYImMnbUluFk5doxn/aU8QT9tMMFc4qPpNwQ1bmNSaHjqbuGnCf62G7PlzEc0a6OJNSeLEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:54.591283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd655ea590f6653a78003c889c07eea26898d588d36241354dd02fa4c383ecae","sha256:e68e7aecbbe7858c6b4f9f9681f139a9f9bedca0482e8c194a2e9918ac829fa2"],"state_sha256":"5eecded97d127a5448e29d01ef9b824f3108763676efc544cbbb2e93338c5e88"}