The analytic theory of Poincaré series and Maass cusp forms and their L-functions for SL3(ℤ) has, so far, been limited to the spherical Maass forms, i.e. elements of a spectral basis for L2(SL3(ℤ)\PSL3(ℝ)/SO3(ℝ)). I will describe the Maass cusp forms of L2(SL3(ℤ)\PSL3(ℝ)) which are minimal with respect to the action of the Lie algebra and give a (relatively) simple method for constructing Kuznetsov-type trace formulas by considering Fourier coefficients of certain Poincaré series. In recent work with Valentin Blomer, we have extended our proof of spectral-aspect subconvexity for L-functions of SL3(ℤ) Maass forms to the non-spherical case, and I will discuss the structure of that proof, as well.
This video is part of the Institute for Advanced Study‘s Number theory seminar.
