Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

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...

Spectra of elements in the group ring of SU(2)

Alex GamburdDmitry JakobsonPeter Sarnak — 1999

Journal of the European Mathematical Society

We present a new method for establishing the ‘‘gap” property for finitely generated subgroups of SU ( 2 ) , providing an elementary solution of Ruziewicz problem on S 2 as well as giving many new examples of finitely generated subgroups of SU ( 2 ) with an explicit gap. The distribution of the eigenvalues of the elements of the group ring 𝐑 [ SU ( 2 ) ] in the N -th irreducible representation of SU ( 2 ) is also studied. Numerical experiments indicate that for a generic (in measure) element of 𝐑 [ SU ( 2 ) ] , the “unfolded” consecutive spacings...

Page 1

Download Results (CSV)