{"paper":{"title":"Computation of the secondary zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Juan Arias de Reyna","submitted_at":"2020-06-08T18:40:54Z","abstract_excerpt":"The secondary zeta function $Z(s)=\\sum_{n=1}^\\infty\\alpha_n^{-s}$, where $\\rho_n=\\frac12+i\\alpha_n$ are the zeros of zeta with $\\Im(\\rho)>0$, extends to a meromorphic function on the hole complex plane. If we assume the Riemann hypothesis the numbers $\\alpha_n=\\gamma_n$, but we do not assume the RH. We give an algorithm to compute the analytic prolongation of the Dirichlet series $Z(s)=\\sum_{n=1}^\\infty \\alpha_n^{-s}$, for all values of $s$ and to a given precision."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04869","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/2006.04869/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"}