{"paper":{"title":"A criterion related to the Riemann Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Helmut Maier, Michael Th. Rassias","submitted_at":"2017-05-28T09:40:13Z","abstract_excerpt":"A crucial role in the Nyman-Beurling-B\\'aez-Duarte approach to the Riemann Hypothesis is played by the distance \\[ d_N^2:=\\inf_{A_N}\\frac{1}{2\\pi}\\int_{-\\infty}^\\infty\\left|1-\\zeta A_N\\left(\\frac{1}{2}+it\\right)\\right|^2\\frac{dt}{\\frac{1}{4}+t^2}\\:, \\] where the infimum is over all Dirichlet polynomials $$A_N(s)=\\sum_{n=1}^{N}\\frac{a_n}{n^s}$$ of length $N$. In this paper we investigate $d_N^2$ under the assumption that the Riemann zeta function has four non-trivial zeros off the critical line. Thus we obtain a criterion for the non validity of the Riemann Hypothesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09918","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":""},"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"}