{"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. We focus on the case $k=2$ and we show that the sine serie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5871","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}