{"paper":{"title":"Exploring Riemann's Functional Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Michael Milgram","submitted_at":"2015-10-20T18:59:25Z","abstract_excerpt":"An equivalent, but variant form of the Riemann functional equation is explored, and several discoveries are made. Properties of the Riemann zeta function $\\zeta(s)$ from which a necessary and sufficient condition for the existence of zeros in the critical strip are deduced. This in turn, by an indirect route, eventually produces a simple, solvable, differential equation for $arg(\\zeta(s))$ on the critical line $s=1/2+i\\rho$, the consequences of which are explored, and the \"LogZeta\" function is introduced. A singular linear transform between the real and imaginary components of $\\zeta$ and $\\ze"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06333","kind":"arxiv","version":3},"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"}