{"paper":{"title":"Self-intersections of the Riemann zeta function on the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlo Morpurgo, Luigi Fontana, Victor Castillo-Garate, William Banks","submitted_at":"2012-10-31T21:55:26Z","abstract_excerpt":"We show that the Riemann zeta function \\zeta\\ has only countably many self-intersections on the critical line, i.e., for all but countably many z in C the equation \\zeta(1/2+it)=z has at most one solution t in R. More generally, we prove that if F is analytic in a complex neighborhood of R and locally injective on R, then either the set {(a,b) in R^2:a \\ne b and F(a)=F(b)} is countable, or the image F(R) is a loop in C."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0044","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"}