Nonspherical Poincaré series, cusp forms and Lfunctions for GL(3)
Nonspherical Poincaré series, cusp forms and Lfunctions for GL(3)

Jack Buttcane, University of Buffalo
IAS Room S101
The analytic theory of Poincaré series and Maass cusp forms and their Lfunctions for SL(3,Z) has, so far, been limited to the spherical Maass forms, i.e. elements of a spectral basis for L^2(SL(3,Z)\PSL(3,R)/SO(3,R)). I will describe the Maass cusp forms of L^2(SL(3,Z)\PSL(3,R)) which are minimal with respect to the action of the Lie algebra and give a (relatively) simple method for constructing Kuznetsovtype trace formulas by considering Fourier coefficients of certain Poincaré series. In recent work with Valentin Blomer, we have extended our proof of spectralaspect subconvexity for Lfunctions of SL(3,Z) Maass forms to the nonspherical case, and I will discuss the structure of that proof, as well.