{
  "id": "1608.05746",
  "version": "v1",
  "published": "2016-08-19T22:00:45.000Z",
  "updated": "2016-08-19T22:00:45.000Z",
  "title": "Sup-norm of eigenfunction of finitely many Hecke operators",
  "authors": [
    "Subhajit Jana"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\phi$ be a Laplace eigenfunction on a compact hyperbolic surface attached to an order in a quaternion algebra. Assuming that $\\phi$ is an eigenfunction of Hecke operators at a \\emph{fixed finite} collection of primes, we prove an $L^\\infty$-norm bound for $\\phi$ that improves upon the trivial estimate by a power of the logarithm of the eigenvalue. We have constructed an amplifier whose length depends on the support of the amplifier on Hecke trees. We have used a method of B\\'erard to improve the archimedean amplification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-19T22:00:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F12",
      "11F72"
    ],
    "keywords": [
      "hecke operators",
      "compact hyperbolic surface",
      "archimedean amplification",
      "laplace eigenfunction",
      "quaternion algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}