Ph.D Student Ph.D Thesis Beit-Aharon Or A Voronoi Summation Formula for the Fourier Coefficients of Maass Forms on the Three Dimensional Hyperbolic Space Department of Mathematics PROF. Ehud Moshe Baruch ASSOCIATE PROF. Omer Offen Abstract

We prove a Voronoi summation formula for the Fourier coefficients of Maass cusp forms on the three dimensional hyperbolic space. Starting with a Maass cusp form for which is a Hecke eigenform we construct an automorphic form on . We show that the Voronoi summation formula follows from the automorphic property of the form we constructed, by expressing the fact that its value at the identity matrix equals its value at the Weyl element, in terms of the corresponding Fourier-Whittaker expansion. To get the explicit formula we use a kernel formula for the action of the Weyl element in the Whittaker model of principal series representations of .
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