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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 $"},"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":"1705.09969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-28T17:51:47Z","cross_cats_sorted":[],"title_canon_sha256":"53c2cc7264c345fd65beb022402237009db2bbe758273dac8874a34b9da7d453","abstract_canon_sha256":"1ec36fba7b7d42ceb4421afb1d8f8ca7646b1d1779311ba5fcc1a2e48e1aadd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:34.069169Z","signature_b64":"cGRyATNlADJ/j+XmuZF6je1U9j0a2TWzA/jSpGMbt0JU//f+Z6Vv95aNTU4l4ka3uoKrkfFbUmpw7BAvxAPpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e98046781e33fb04cfd7f80c956af53e49ca97f2f15f8bddc666a5db566f613","last_reissued_at":"2026-05-18T00:43:34.068606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:34.068606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $s=1$. 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