{"paper":{"title":"On certain zeta functions associated with Beatty sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"William D. Banks","submitted_at":"2017-05-28T17:51:47Z","abstract_excerpt":"Let $\\alpha>1$ be an irrational number of finite type $\\tau$. In this paper, we introduce and study a zeta function $Z_\\alpha^\\sharp(r,q;s)$ that is closely related to the Lipschitz-Lerch zeta function and is naturally associated with the Beatty sequence ${\\mathcal B}(\\alpha):=(\\lfloor\\alpha m\\rfloor)_{m\\in{\\mathbb N}}$. If $r$ is an element of the lattice ${\\mathbb Z}+{\\mathbb Z}\\alpha^{-1}$, then $Z_\\alpha^\\sharp(r,q;s)$ continues analytically to the half-plane $\\{\\sigma>-1/\\tau\\}$ with its only singularity being a simple pole at $s=1$. If $r\\not\\in{\\mathbb Z}+{\\mathbb Z}\\alpha^{-1}$, then $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09969","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"}