{"paper":{"title":"The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chan Ieong Kuan, E. Mehmet Kiral, Li-Mei Lim, Thomas A. Hulse","submitted_at":"2011-06-18T02:27:37Z","abstract_excerpt":"From a result of Waldspurger, it is known that the normalized Fourier coefficients $a(m)$ of a half-integral weight holomorphic cusp eigenform $\\f$ are, up to a finite set of factors, one of $\\pm \\sqrt{L(1/2, f, \\chi_m)}$ when $m$ is square-free and $f$ is the integral weight cusp form related to $\\f$ by the Shimura correspondence. In this paper we address a question posed by Kohnen: which square root is $a(m)$? In particular, if we look at the set of $a(m)$ with $m$ square-free, do these Fourier coefficients change sign infinitely often? By partially analytically continuing a related Dirichle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3606","kind":"arxiv","version":5},"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"}