{"paper":{"title":"Zeta distributions generated by Dirichlet series and their (quasi) infinite divisibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Takashi Nakamura","submitted_at":"2022-09-27T08:54:37Z","abstract_excerpt":"Let $a(1) >0$, $a(n) \\ge 0$ for $n \\ge 2$ and $a(n) = O(n^\\varepsilon)$ for any $\\varepsilon >0$, and put $Z(\\sigma + it):= \\sum_{n=1}^\\infty a(n) n^{-\\sigma - it}$ where $\\sigma , t \\in {\\mathbb{R}}$. In the present paper, we show that any zeta distribution whose characteristic function is defined by ${\\mathcal{Z}}_\\sigma (t) :=Z(\\sigma + it)/Z(\\sigma)$ is pretended infinitely divisible if $\\sigma >1$ is sufficiently large. Moreover, we prove that if ${\\mathcal{Z}}_\\sigma (t)$ is an infinitely divisible characteristic function for some $\\sigma_{id} >1$, then ${\\mathcal{Z}}_\\sigma (t)$ is infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13257","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.13257/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}