{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NFXWRYYBV77FCO23YYHLYGW45N","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":"2ea53f42c569fe896547b194af0012877e2cf436d00bab474b7c1ffb0caed50a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-21T13:45:26Z","title_canon_sha256":"e25b8d4ce65da7f4941a2709eba742eb7a2a191130b6b9cfc032717f1b156882"},"schema_version":"1.0","source":{"id":"1411.5871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5871","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5871v1","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5871","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"NFXWRYYBV77F","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFXWRYYBV77FCO23","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFXWRYYB","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:b6a5d483f838af38d990eaf2b783942f293c97c6eefdfc81b4f3eb1b87573500","target":"graph","created_at":"2026-05-18T01:22:03Z","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 $k$ be even. We consider two series $F_k(x)= \\sum_{n=1}^\\infty \\frac{\\sigma_{k-1}(n)}{n^{k+1}} \\sin(2\\pi n x)$ and $G_k(x)= \\sum_{n=1}^\\infty \\frac{\\sigma_{k-1}(n)}{n^{k+1}} \\cos(2\\pi n x)$, where $\\sigma_{k-1}$ is the divisor function. They converge on $\\mathbb{R}$ to continuous functions. In this paper, we examine the differentiability of $F_k$ and $G_k$. These functions are related to Eisenstein series and their (quasi-)modular properties allow us to apply the method proposed by Itatsu in 1981 in the study of the Riemann series. We focus on the case $k=2$ and we show that the sine serie","authors_text":"Izabela Petrykiewicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-21T13:45:26Z","title":"Differentiability of arithmetic Fourier series arising from Eisenstein series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5871","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:bd29668248cd723cb45270bc065785e7d6c72d15a5d9641c26c46f95f1bceb17","target":"record","created_at":"2026-05-18T01:22:03Z","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":"2ea53f42c569fe896547b194af0012877e2cf436d00bab474b7c1ffb0caed50a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-21T13:45:26Z","title_canon_sha256":"e25b8d4ce65da7f4941a2709eba742eb7a2a191130b6b9cfc032717f1b156882"},"schema_version":"1.0","source":{"id":"1411.5871","kind":"arxiv","version":1}},"canonical_sha256":"696f68e301affe513b5bc60ebc1adceb4499267097209c52eea38ed5b9d6b41d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"696f68e301affe513b5bc60ebc1adceb4499267097209c52eea38ed5b9d6b41d","first_computed_at":"2026-05-18T01:22:03.291910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:03.291910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PAzWCnI3VzDBZdpsKt/c/sbDAr4cgm/0hAsxaMqTlHJFSC9cra55V95DCKx9KIhelNRrSMxYp5Mc6Np3Qy6EDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:03.292282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd29668248cd723cb45270bc065785e7d6c72d15a5d9641c26c46f95f1bceb17","sha256:b6a5d483f838af38d990eaf2b783942f293c97c6eefdfc81b4f3eb1b87573500"],"state_sha256":"6fc8ae807cc519629ca3e561b6b4e135d0261e1bc47e1ff3d23722950bbbffbf"}