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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.5871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-21T13:45:26Z","cross_cats_sorted":[],"title_canon_sha256":"e25b8d4ce65da7f4941a2709eba742eb7a2a191130b6b9cfc032717f1b156882","abstract_canon_sha256":"2ea53f42c569fe896547b194af0012877e2cf436d00bab474b7c1ffb0caed50a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:03.292282Z","signature_b64":"PAzWCnI3VzDBZdpsKt/c/sbDAr4cgm/0hAsxaMqTlHJFSC9cra55V95DCKx9KIhelNRrSMxYp5Mc6Np3Qy6EDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"696f68e301affe513b5bc60ebc1adceb4499267097209c52eea38ed5b9d6b41d","last_reissued_at":"2026-05-18T01:22:03.291910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:03.291910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differentiability of arithmetic Fourier series arising from Eisenstein series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Izabela Petrykiewicz","submitted_at":"2014-11-21T13:45:26Z","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. 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