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Quantum Limits of Eisenstein Series and Scattering States

Open Access article
 Printed: Dec 2013
  • Yiannis N. Petridis,
    Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UNITED KINGDOM
  • Nicole Raulf,
    Laboratoire Paul Painleve', U.F.R. de Mathematiques, Universite' Lille 1 Sciences et Technologies, 59 655 Villeneuve d'Ascq CĂ©dex, FRANCE
  • Morten S. Risager,
    Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, DENMARK
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We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak.
Keywords: quantum limits, Eisenstein series, scattering poles quantum limits, Eisenstein series, scattering poles
MSC Classifications: 11F72, 58G25, 35P25 show english descriptions Spectral theory; Selberg trace formula
unknown classification 58G25
Scattering theory [See also 47A40]
11F72 - Spectral theory; Selberg trace formula
58G25 - unknown classification 58G25
35P25 - Scattering theory [See also 47A40]

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