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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"},"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":"1908.07845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-21T13:04:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1157b41fcf1afb31987453094fd5facea217db04932be3238a7a92528bc15afb","abstract_canon_sha256":"3dfaaeb1e989ff959691b5e952d5e2e1d700de2a8493651f54c714483c5c3ea5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:02:26.172863Z","signature_b64":"F7BAagw/DiZxIn8d7nZtZSlBS6Lc3t5iJCyZIP1Oz3MNwWucgpX4ikHiwojRJi7ZH53uYnTKJMvgP1TsT6x5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25535b74be1f755e29b4ae06a2a3a792fd473dd68475bcef9963e58be6b6487f","last_reissued_at":"2026-07-05T06:02:26.172469Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:02:26.172469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $D(\\zeta_{\\mathcal L})=D$. 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