{"paper":{"title":"A few remarks on values of Hurwitz Zeta function at natural and rational arguments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2014-05-24T05:37:48Z","abstract_excerpt":"We exploit some properties of the Hurwitz zeta function $\\zeta (n,x)$ in order to study sums of the form $\\frac{1}{\\pi ^{n}}\\sum_{j=-\\infty}^{\\infty}1/(jk+l)^{n}$ and $\\frac{1}{\\pi ^{n}}\\sum_{j=-\\infty}^{\\infty}(-1)^{j}/(jk+l)^{n}$ for $% 2\\leq n,k\\in \\mathbb{N},$ and integer $l\\leq k/2$. We show that these sums are algebraic numbers. We also show that $1<n\\in \\mathbb{N}$ and $p\\in \\mathbb{Q\\cap (}0,1\\mathbb{)}$ $:$ the numbers $(\\zeta (n,p)+(-1)^{n}\\zeta (n,1-p))/\\pi ^{n}$ are algebraic. On the way we find polynomials $s_{m}$ and $c_{m}$ of order respectively $2m+1$ and $2m+2$ such that their"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6270","kind":"arxiv","version":2},"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"}