{"paper":{"title":"Hurwitz integrality of power series expansion of the sigma function for a plane curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Yoshihiro \\^Onishi","submitted_at":"2015-10-11T02:45:11Z","abstract_excerpt":"This paper shows Hurwitz integrality of the coefficients of expansion at the origin of the sigma function \\(\\sigma(u)\\) associated to a certain plane curve which should be called a plane telescopic curve. For the prime \\(2\\), the expansion of \\(\\sigma(u)\\) is not Hurwitz integral, but \\(\\sigma(u)^2\\) is. This paper clarifies the precise structure of this phenomenon. Throughout the paper, computational examples for the trigonal genus three curve (\\((3,4)\\)-curve) \\(y^3+(\\mu_1x+\\mu_4)y^2+(\\mu_2x^2+\\mu_5x+\\mu_8)y=x^4+\\mu_3x^3+\\mu_6x^2+\\mu_9x+\\mu_{12}\\) (\\(\\mu_j\\) are constants) are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03002","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"}