{"paper":{"title":"Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jay Jorgenson, Joshua S. Friedman, Lejla Smajlovic","submitted_at":"2017-01-24T13:46:51Z","abstract_excerpt":"Let $\\Lambda = \\{\\lambda_{k}\\}$ denote a sequence of complex numbers and assume that that the counting function $#\\{\\lambda_{k} \\in \\Lambda : | \\lambda_{k}| < T\\} =O(T^{n})$ for some integer $n$. From Hadamard's theorem, we can construct an entire function $f$ of order at most $n$ such that $\\Lambda$ is the divisor $f$. In this article we prove, under reasonably general conditions, that the superzeta function $\\Z_{f}(s,z)$ associated to $\\Lambda$ admits a meromorphic continuation. Furthermore, we describe the relation between the regularized product of the sequence $z-\\Lambda$ and the function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06869","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"}