{"paper":{"title":"A canonical system of differential equations arising from the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Masatoshi Suzuki","submitted_at":"2012-04-09T08:30:44Z","abstract_excerpt":"This paper has two main results, which relate to a criteria for the Riemann hypothesis via the family of functions $\\Theta_\\omega(z)=\\xi(1/2-\\omega-iz)/\\xi(1/2+\\omega-iz)$, where $\\omega>0$ is a real parameter and $\\xi(s)$ is the Riemann xi-function. The first main result is necessary and sufficient conditions for $\\Theta_\\omega$ to be a meromorphic inner function in the upper half-plane. It is related to the Riemann hypothesis directly whether $\\Theta_\\omega$ is a meromorphic inner function. In comparison with this, a relation of the Riemann hypothesis and the second main result is indirect. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1827","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"}