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

2019/11/28 by Walkoe, Iver
#11F55 (Primary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1911.12838

Abstract

We extend Lax-Phillips' theorem on discreteness of pseudo-cuspforms, in the style of Colin de Verdière'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 several ℚ-rank one cases, again following Colin de Verdière, as opposed to the semigroup-oriented viewpoint of Lax-Phillips and W. Mueller.

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