{"paper":{"title":"Essential singularities of fractal zeta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"(2) University of Zagreb), Darko \\v{Z}ubrini\\'c (2) ((1) University of California, Goran Radunovi\\'c (2), Michel L. Lapidus (1), Riverside","submitted_at":"2019-08-21T13:04:53Z","abstract_excerpt":"We study the essential singularities of geometric zeta functions $\\zeta_{\\mathcal L}$, associated with bounded fractal strings $\\mathcal L$. For any three prescribed real numbers $D_{\\infty}$, $D_1$ and $D$ in $[0,1]$, such that $D_{\\infty}<D_1\\le D$, we construct a bounded fractal string $\\mathcal L$ such that $D_{\\rm par}(\\zeta_{\\mathcal L})=D_{\\infty}$, $D_{\\rm mer}(\\zeta_{\\mathcal L})=D_1$ and $D(\\zeta_{\\mathcal L})=D$. Here, $D(\\zeta_{\\mathcal L})$ is the abscissa of absolute convergence of $\\zeta_{\\mathcal L}$, $D_{\\rm mer}(\\zeta_{\\mathcal L})$ is the abscissa of meromorphic continuation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07845","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07845/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"}