{"paper":{"title":"Effective sup-norm bounds on average for cusp forms of even weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jay Jorgenson, Joshua S. Friedman, J\\\"urg Kramer","submitted_at":"2018-01-17T16:33:16Z","abstract_excerpt":"Let $\\Gamma\\subset\\mathrm{PSL}_{2}(\\mathbb{R})$ be a Fuchsian subgroup of the first kind acting on the upper half-plane $\\mathbb{H}$. Consider the $d_{2k}$-dimensional space of cusp forms $\\mathcal{S}_{2k}^{\\Gamma}$ of weight $2k$ for $\\Gamma$, and let $\\{f_{1},\\ldots,f_{d_{2k}}\\}$ be an orthonormal basis of $\\mathcal{S}_{2k}^{\\Gamma}$ with respect to the Petersson inner product. In this paper we will give effective upper and lower bounds for the supremum of the quantity $S_{2k}^{\\Gamma}(z):=\\sum_{j=1}^{d_{2k}}\\vert f_{j}(z)\\vert^{2}\\,\\mathrm{Im}(z)^{2k}$ as $z$ ranges through $\\mathbb{H}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05740","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"}