{"paper":{"title":"A note on the Fourier coefficients of a Cohen-Eisenstein series","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Srilakshmi Krishnamoorthy","submitted_at":"2015-04-15T17:00:36Z","abstract_excerpt":"We prove a formula for the coefficients of a weight $3/2$ Cohen-Eisenstein series of square-free level $N$. This formula generalizes a result of Gross and in particular, it proves a conjecture of Quattrini. Let $l$ be an odd prime number. For any elliptic curve $E$ defined over $\\mathbb{Q}$ of rank zero and square-free conductor $N$, if $l \\mid |E(\\mathbb{Q})|$, under certain conditions on the Shafarevich-Tate group $III_D$, we show that $l$ divides $|III_D|$ if and only if $l$ divides the class number $h(-D)$ of $\\mathbb{Q}(\\sqrt{-D}).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03971","kind":"arxiv","version":2},"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"}