{"paper":{"title":"Uniform sup-norm bounds on average for cusp forms of higher weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jay Jorgenson, Joshua S. Friedman, Jurg Kramer","submitted_at":"2013-05-06T22:43:37Z","abstract_excerpt":"Let $\\Gamma\\subseteq\\mathrm{PSL}_{2}(\\mathbb{R})$ be a Fuchsian subgroup of the first kind acting on the upper half-plane $\\mathbb{H}$. Consider the $d$-dimensional space of cusp forms $\\mathcal{S}_{k}^{\\Gamma}$ of weight $2k$ for $\\Gamma$, and let $\\{f_{1},\\ldots,f_{d}\\}$ be an orthonormal basis of $\\mathcal{S}_{k}^{\\Gamma}$ with respect to the Petersson inner product. In this paper we show that the sup-norm of the quantity $S_{k}^{\\Gamma}(z):=\\sum_{j=1}^{d}| f_{j}(z)|^{2}\\,\\mathrm{Im}(z)^{2k}$ is bounded as $O_{\\Gamma}(k)$ in the cocompact setting, and as $O_{\\Gamma}(k^{3/2})$ in the cofinit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1348","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"}