{"paper":{"title":"Non-zero coefficients of half-integral weight modular forms mod $\\ell$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ben Green, Jo\\\"el Bella\\\"iche, Kannan Soundararajan","submitted_at":"2017-04-24T20:00:58Z","abstract_excerpt":"We obtain new lower bounds for the number of Fourier coefficients of a weakly holomorphic modular form of half-integral weight not divisible by some prime $\\ell$. Among the applications of this we show that there are $\\gg \\sqrt{X}/\\log \\log X$ integers $n \\leq X$ for which the partition function $p(n)$ is not divisible by $\\ell$, and that there are $\\gg \\sqrt{X}/\\log \\log X$ values of $n \\leq X$ for which $c(n)$, the $n$th Fourier coefficient of the $j$-invariant, is odd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07440","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"}