{"paper":{"title":"Hybrid sup-norm bounds for Maass newforms of powerful level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SP"],"primary_cat":"math.NT","authors_text":"Abhishek Saha","submitted_at":"2015-09-24T19:47:16Z","abstract_excerpt":"Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\\chi$ and Laplace eigenvalue $\\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer such that $N_0^2 |N$. Let $M$ denote the conductor of $\\chi$ and define $M_1= M/\\gcd(M,N_1)$. In this paper, we prove the bound $|f|_\\infty$ $\\ll_{\\epsilon}$ $N_0^{1/6 + \\epsilon} N_1^{1/3+\\epsilon} M_1^{1/2} \\lambda^{5/24+\\epsilon}$, which generalizes and strengthens previously known upper bounds for $|f|_\\infty$.\n  This is the first time a hybrid bound (i.e., involving both "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07489","kind":"arxiv","version":4},"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"}