טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBeit-Aharon Or
SubjectA Voronoi Summation Formula for the Fourier Coefficients
of Maass Forms on the Three Dimensional Hyperbolic
Space
DepartmentDepartment of Mathematics
Supervisors Professor Ehud Moshe Baruch
Professor Omer Offen
Full Thesis textFull thesis text - English Version


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 .