{"paper":{"title":"Bounding sup-norms of cusp forms of large level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Roman Holowinsky, Valentin Blomer","submitted_at":"2008-08-11T15:21:11Z","abstract_excerpt":"Let f be an $L^2$-normalized weight zero Hecke-Maass cusp form of square-free level N, character $\\chi$ and Laplacian eigenvalue $\\lambda\\geq 1/4$. It is shown that $\\| f \\|_{\\infty} \\ll_{\\lambda} N^{-1/37}$, from which the hybrid bound $\\|f \\|_{\\infty} \\ll \\lambda^{1/4} (N\\lambda)^{-\\delta}$ (for some $\\delta > 0$) is derived. The first bound holds also for $f = y^{k/2}F$ where F is a holomorphic cusp form of weight k with the implied constant now depending on k."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1525","kind":"arxiv","version":3},"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"}