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Quantum Limits of Eisenstein Series and Scattering States

Published online by Cambridge University Press:  20 November 2018

Yiannis N. Petridis ,
Nicole Raulf  and
Morten S. Risager
Yiannis N. Petridis
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom e-mail: i.petridis@ucl.ac.uk
Nicole Raulf
Affiliation:
Laboratoire Paul Painlevé, U.F.R. de Mathematiques, Université Lille 1 Sciences et Technologies, 59 655 Villeneuve d’Ascq Cédex, France e-mail: e-mail: nicole.raulf@math.univ-lille1.fr
Morten S. Risager
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Denmark e-mail: risager@math.ku.dk
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Abstract.

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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

11F7258G2535P25quantum limitsEisenstein seriesscattering poles
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 814 - 826
Copyright
Copyright © Canadian Mathematical Society 2013

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