{"paper":{"title":"Estimates of Fourier coefficients of integral and half-integral weight cusp forms associated to cofinite Fuchsian subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anilatmaja Aryasomayajula","submitted_at":"2018-08-16T11:06:21Z","abstract_excerpt":"Let $\\G\\subset \\mathrm{SL}_{2}(\\R)$ be a cofinite Fuchsian subgroup, and let $i\\infty$ be a cusp of $\\G$. For $k\\in\\Z_{\\geq 0}$, let $\\Sk$ denote the complex vector space of cusp forms of weight-$k$, with respect to the Fuchsian subgroup $\\G$. Let $f\\in\\Sk$ be a cusp form of weight-$k$, which is normalized, with respect to the Petersson inner-product on $\\Sk$. For any $n\\in\\Z_{\\geq 1}$, let $a_{n}$ denote the $n$-th Fourier coefficient of $f$ at $i\\infty$. Then, for any $k\\in\\Z_{\\geq 5}$, we show that \\begin{align*} \\big|a_{n}\\big|=O_{f,\\G}\\big(n^{\\frac{k-1}{2}+\\frac{2}{k}}\\big), \\end{align*} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05416","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"}