Spectral decomposition of pseudo-cuspforms, and meromorphic continuation of Eisenstein series, on Q-rank one arithmetic quotients

Walkoe, Iver2019-08-202019-08-202019-05https://hdl.handle.net/11299/206351University of Minnesota Ph.D. dissertation. May 2019. Major: Mathematics. Advisor: Paul Garrett. 1 computer file (PDF); vii, 171 pages.In this paper, we extend Lax-Phillips’ discreteness of pseudo-cuspforms, in the style of Colin de Verdiere’s use of the Friedrichs self-adjoint extension of a restriction of the Laplace-Beltrami operator, as opposed to the use of semigroup methods. We use this to prove meromorphic continuation of Eisenstein series in the Q-rank one case, again following Colin de Verdiere, as opposed to the semigroup-oriented viewpoint of Lax-Phillips and W. Mueller.enarithmetic quotientsEisenstein seriesmeromorphic continuationpseudo-cuspformsSpectral decomposition of pseudo-cuspforms, and meromorphic continuation of Eisenstein series, on Q-rank one arithmetic quotientsThesis or Dissertation