{"paper":{"title":"Jacobi inversion formulae for a curve in Weierstrass normal form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP","nlin.SI"],"primary_cat":"math.AG","authors_text":"Jiyro Komeda, Shigeki Matsutani","submitted_at":"2018-05-28T05:05:26Z","abstract_excerpt":"We consider a pointed curve $(X,P)$ which is given by the Weierstrass normal form, $y^r + A_{1}(x) y^{r-1} + A_{2}(x) y^{r-2} +\\cdots + A_{r-1}(x) y + A_{r}(x)$ where $x$ is an affine coordinate on $\\mathbb{P}^1$, the point $\\infty$ on $X$ is mapped to $x=\\infty$, and each $A_j$ is a polynomial in $x$ of degree $\\leq js/r$ for a certain coprime positive integers $r$ and $s$ ($r<s$) so that its Weierstrass non-gap sequence at $\\infty$ is a numerical semigroup. It is a natural generalization of Weierstrass' equation in the Weierstrass elliptic function theory. We investigate such a curve and sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10771","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"}