Equidistribution of cusp forms on ${\rm PSL}_2({\bf Z})\backslash {\rm PSL}_2({\bf R})$

Dmitri Jakobson

Displaying similar documents to “Equidistribution of cusp forms on ${PSL}_{2} (𝐙) ∖ {PSL}_{2} (𝐑)$ ”

Quantum unique ergodicity for Eisenstein series on $P S L_{2} (ℤ ∖ P S L_{2} (ℝ)$

Dmitry Jakobson (1994)

Annales de l'institut Fourier

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In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on $P S L_{2} (ℤ) ∖ P S L_{2} (ℝ)$ . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for $P S L_{2} (ℤ) ∖ ℍ$ . 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 $S L_{2} (ℝ)$ . In the proof the key estimates come...