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Quantum unique ergodicity for Eisenstein series on P S L 2 ( P S L 2 ( )

Dmitry Jakobson (1994)

Annales de l'institut Fourier

In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on P S L 2 ( ) P S L 2 ( ) . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for P S L 2 ( ) . The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of S L 2 ( ) . In the proof the key estimates come from applying...

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