{"paper":{"title":"Real inflection points of real linear series on an elliptic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Cristhian Garay L\\'opez, Ethan Cotterill","submitted_at":"2018-04-18T01:47:23Z","abstract_excerpt":"Given a real elliptic curve $E$ with non-empty real part and $[D]\\in \\mbox{Pic}^2 E$ its $g_2^1$, we study the real inflection points of distinguished subseries of the complete real linear series $|\\mathcal{L}_\\mathbb{R}(kD)|$ for $k\\geq 3$. We define {\\it key polynomials} whose roots index the ($x$-coordinates of) inflection points of the linear series, away from the points where $E$ ramifies over $\\mathbb{P}^1$. These fit into a recursive hierarchy, in the same way that division polynomials index torsion points.\n  Our study is motivated by, and complements, an analysis of how inflectionary l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06524","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"}