{"paper":{"title":"Maass forms and the mock theta function $f(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Dunn, Scott Ahlgren","submitted_at":"2018-06-04T16:30:41Z","abstract_excerpt":"Let $f(q)=1+\\sum_{n=1}^{\\infty} \\alpha(n)q^n$ be the well-known third order mock theta of Ramanujan. In 1964, George Andrews proved an asymptotic formula of the form $$\\alpha(n)= \\sum_{c\\leq\\sqrt{n}} \\psi(n)+O_\\epsilon\\left(n^\\epsilon\\right),$$ where $\\psi(n)$ is an expression involving generalized Kloosterman sums and the $I$-Bessel function. Andrews conjectured that the series converges to $\\alpha(n)$ when extended to infinity, and that it does not converge absolutely. Bringmann and Ono proved the first of these conjectures. Here we obtain a power savings bound for the error in Andrews' form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01187","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"}