{"paper":{"title":"Landen transforms as families of (commuting) rational self-maps of projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Joseph H. Silverman, Michael Joyce, Shu Kawaguchi","submitted_at":"2013-08-24T19:36:15Z","abstract_excerpt":"The classical (m,k)-Landen transform F_{m,k} is a self-map of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m'th roots of unity. Identifying the set of rational maps of degree d with an affine open subset of P^{2d+1}, we prove that F_{m,0} induces a dominant rational self-map R_{d,m,0} of P^{2d+1} of algebraic degree m, and for 0 < k < m, the transform F_{m,k} induces a dominant rational self-map R_{d,m,k} of algebraic degree m of a certain hyperplane in P^{2d+1}. We show in all cases that R_{d,m,k} extends nicely to a map of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5355","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"}