{"paper":{"title":"Ternary Quadratic Forms And Half-Integral Weight Modular Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alia Hamieh","submitted_at":"2016-09-23T03:21:40Z","abstract_excerpt":"Let $k$ be a positive integer such that $k\\equiv3\\mod4$, and let $N$ be a positive square-free integer. In this paper, we compute a basis for the two-dimensional subspace $S_{\\frac{k}{2}}(\\Gamma_{0}(4N),F)$ of half-integral weight modular forms associated, via the Shimura correspondence, to a newform $F\\in S_{k-1}(\\Gamma_{0}(N))$, which satisfies $L(F,\\frac{1}{2})\\neq0$. This is accomplished by using a result of Waldspurger, which allows one to produce a basis for the forms that correspond to a given $F$ via local considerations, once a form in the Kohnen space has been determined"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07218","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"}