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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"},"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":"1405.6270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-24T05:37:48Z","cross_cats_sorted":[],"title_canon_sha256":"1dda0f0f002917ae73d58bfd971b4311dba6dd54b0a44b6813b5ba086f900901","abstract_canon_sha256":"e46f249850068ddab78be67b1c55ff96a1e57362d3bc7ac6e1f19f49bc16ec58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:59.999514Z","signature_b64":"7/5eNRNcu2iji4KO0QLCEFwJCtULM8B2SIzO61U0aEqaoQsv4P8Nx8TfI6q0A7mL/MiPiDkwXKfam1QnS0EWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4367f6d769688ce9bfc3d6b0ff2310a4232198a0052a71b556a45ae75a90991b","last_reissued_at":"2026-05-18T02:31:59.998955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:59.998955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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