Sands, Adrienne2020-11-172020-11-172020-09https://hdl.handle.net/11299/217155University of Minnesota Ph.D. dissertation. 2020. Major: Mathematics. Advisor: Paul Garrett. 1 computer file (PDF); 92 pages.We construct an automorphic Hamiltonian which has purely discrete spectrum on $L^2\left(SL_r(\Z)\backslash SL_r(\R)/SO(r,\R)\right)$, identify its ground state, and show how it can characterize a nuclear Fr\'echet automorphic Schwartz space.enAutomorphic formsAutomorphic HamiltonianAutomorphic Schwartz spaceDegenerate Eisenstein seriesEpstein zeta functionsThesis or Dissertation