{"paper":{"title":"Heat kernel approach for sup-norm bounds for cusp forms of integral and half integral weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anilatmaja Aryasomayajula","submitted_at":"2015-06-29T03:17:15Z","abstract_excerpt":"In this article, using the heat kernel approach from \\cite{bouche}, we derive sup-norm bounds for cusp forms of integral and half integral weight. Let $\\Gamma\\subset \\mathrm{PSL}_{2}(\\mathbb{R})$ be a cocompact Fuchsian subgroup of first kind. For $k\\in\\frac{1}{2}\\mathbb{Z}$ (or $k\\in 2\\mathbb{Z}$), let $S^{k}(\\Gamma)$ denote the complex vector space of weight-$k$ cusp forms. Let $\\lbrace f_{1},\\ldots,f_{j_{k}} \\rbrace$ denote an orthonormal basis of $S^{k}(\\Gamma)$. In this article, we show that as $k\\rightarrow \\infty,$ the sup-norm for $\\sum_{i=1}^{j_{k}}y^{k}|f_{i}(z)|^{2}$ is bounded by $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08497","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"}