Displaying similar documents to “Quantum unique ergodicity for Eisenstein series on P S L 2 ( ℤ ∖ P S L 2 ( ℝ ) ”

Equidistribution of cusp forms on PSL 2 ( 𝐙 ) ∖ PSL 2 ( 𝐑 )

Dmitri Jakobson (1997)

Annales de l'institut Fourier

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We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on PSL 2 ( Z ) ∖ PSL 2 ( R ) . This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on PSL 2 ( Z ) ∖ H .

The reciprocal of the beta function and G L ( n , ℝ ) Whittaker functions

Eric Stade (1994)

Annales de l'institut Fourier

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In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself. We then apply our new formula to the study of G L ( n , ℝ ) Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral...