{
  "id": "2111.09923",
  "version": "v2",
  "published": "2021-11-18T19:33:00.000Z",
  "updated": "2022-04-08T16:02:08.000Z",
  "title": "Hybrid bounds for the sup-norm of automorphic forms in higher rank",
  "authors": [
    "Radu Toma"
  ],
  "comment": "28 pages (previously 17). This version substantially improves the first one with new, more general theorems. The title and abstract have been changed accordingly. Several clarifications were added. Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be a central division algebra of prime degree $p$ over $\\mathbb{Q}$. We obtain subconvex hybrid bounds, uniform in both the eigenvalue and the discriminant, for the sup-norm of Hecke-Maass forms on the compact quotients of $\\operatorname{SL}_p(\\mathbb{R})/\\operatorname{SO}(p)$ by unit groups of orders in $A$. The exponents in the bounds are explicit and polynomial in $p$. We also prove subconvex hybrid bounds in the case of certain Eichler-type orders in division algebras of arbitrary odd degree.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-08T16:02:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55",
      "11F72",
      "11D45",
      "11R52"
    ],
    "keywords": [
      "higher rank",
      "automorphic forms",
      "subconvex hybrid bounds",
      "central division algebra",
      "arbitrary odd degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}